AGEC FINAL P1

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. The Excel solution and the answer and sensitivity report are shown below. Aunt Anastasia feels that her prices are too low, particularly for her eggs. How much would her profit have to increase on the eggs before it is profitable for her to make and sell eggs?

$1.00

Which of these formulations of the budget constraint is correct? Assume that there are 20 students in this semesters MBA class. A + B + C + D + E ≤ 20 $15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250 $750A + $25B + $15,000C + $10D + $5E ≤ $56,250 20A + 20B + C + 20D + 20E ≤ $56,250

$15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit?

$380

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

$45,000

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the optimal weekly profit?

$800

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time is a constant 4 minutes. What is the average number of cars in line?

.133

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time averages 4 minutes with a standard deviation of 1 minute, but the wash time is not defined by any distribution. What is the average number of cars in line?

.142

The following data represents quarterly sales of lawnmowers. What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)

.25

A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. The probability that the system is idle is:

.40.

Binary variables are:

0 or 1 only.

In a ________ integer model, the solution values of the decision variables are 0 or 1. total 0-1 mixed all of the above

0-1

_______ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

________ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

In a ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

If the probability of an event is 0.36, what random number range specifies this properly?

0.30 - 0.40

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: The optimal quantity of the three products and resulting revenue for Taco Loco is:

1.45 Z, 8.36 Y, and 0 Z for $129.09.

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. How many constraints are required to model this as a linear program?

10

Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processed within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. What is the minimum average processing rate (in truckloads per hour) that must be designed for the machine in order to ensure that the cages will be processed, on the average, in 30 minutes or less? Assume processing time is exponentially distributed

10 trucks per hour

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. Llamas are pack animals and the owner occasionally has them tote supplies from the fruit trees down to the hay stand. What is the shortest route between the two?

155'

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix?

17.78 to 30 pounds

Which of the following could not be a linear programming problem constraint?

1A + 2B ≠ 3

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. Determine the average time that a snowplow is out of service.

2.64 hours

A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 10-minute intervals, the following probability distribution and random number assignments developed. Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?

24

Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

24

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. The horse decides that a small system of trails would be perfect for connecting his points of interest, the Grass, Barn, Hay and Pond along with the Oak. What is the minimal total path length for this construction project?

270'

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. The llamas decide that a small system of trails would be perfect for connecting their points of interest, the Fruit, Barn, Hay, Shade, Pond and the Oak. What is the minimal total path length for this construction project?

270'

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z?

28.73

Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame: Use a 2-period moving average to forecast demand for period 7.

290

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

2R + 4D ≤ 480

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. Which of the following is not a feasible solution?

300 L and 200 D

A rendering plant wishes to use the data (sales records from a few local businesses and the month of the year) to help determine their supply level for the coming months. The records shown in the table provide an excellent opportunity for you to assist them with their forecasting. What is the three-period weighted moving average for July using the weights 0.5 (most recent), 0.3, and 0.2?

45.6

What is the 95% confidence interval width for a sample with a mean of 50 and a standard deviation of 14 based on 75 observations?

46.83, 53.17)

A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:

4x1 + 3x2 + 2x3 ≤ 24

Given the following linear program that maximizes revenue: What is the maximum revenue at the optimal solution?

$160

In a(n) ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend is reflected.

1

A graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he's cooking an order, they have to wait until he's completed the current order. He has simulated 5 orders. Average customer waiting time is:

1 minute

Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches.

13

Balanced transportation problems have which of the following type of constraints?

=

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit? A) $380 B) $400 C) $420 D) $440

A

When systematically formulating a linear program, the first step is to: A) construct the objective function. B) formulate the constraints. C) identify the decision variables. D) identify the parameter values.

C

Compared to blending and product mix problems, transportation problems are unique because: A) they maximize profit. B) the constraints are all equality constraints with no "≤" or "≥" constraints. C) they contain fewer variables. D) the solution values are always integers

D

The branch and bound method of solving linear integer programming problems is: A) an integer method. B) a relaxation method. C) a graphical solution. D) an enumeration method.

D

A mixed integer program has only integers as a solution they are simply mixed, as opposed to an integer program where they are specific to the decision variables. True or False

False

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

False

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

False

In a mixed integer model, the solution values of the decision variables are 0 or 1.

False

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.

False

is not part of a Monte Carlo simulation

Finding an optimal solution

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following points is not feasible?

G

Which of the following are assumptions or requirements of the transportation problem?

Goods are the same, regardless of source

indicates a forecast is biased high.

Large -

is absolute error as a percentage of demand.

MAPD

The ________ process is analogous to gambling devices.

Monte Carlo

use management judgment, expertise, and opinion to make forecasts.

Qualitative methods

T/F: The divisibility assumption is violated by integer programming.

T

The three types of integer programming models are total, 0-1, and mixed. True or False

TRUE

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Copied below is a portion of the answer report that shows the constraints related to the faculty assignment. Which of these statements is best according to the answer report?

Tim is assigned to teach two courses

methods assume that what has occurred in the past will continue to occur in the future.

Time series

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

True

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem.

True

The divisibility assumption is violated by integer programming

True

The three types of integer programming models are total, 0-1, and mixed.

True

The constraint for the South Asia demand region is:

X13 + X23 + X33 + X43 = 7.

The objective function is

answer with 3 then 4 + 3

In a transportation problem, items are allocated from sources to destinations:

at a minimum cost.

In a single-server queuing model, L represents the

average number of customers waiting and being served

In a multiperiod scheduling problem, the production constraint usually takes the form of:

beginning inventory - demand + production = ending inventory

The ________ method is based on the principle that the total set of feasible solutions can be partitioned into smaller subsets of solutions.

branch and bound

The indicator that results in total revenues being equal to total cost is called the:

break-even point.

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint.

conditional

If the price increases, but fixed and variable costs do not change, the break-even point

decreases.

In a transshipment problem, items may be transported:

from destination to destination. from one transshipment point to another. directly from sources to destinations. Correct All of these

If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch?

heating and ventilation systems

Which of the following will not decrease system utilization?

increase in arrival rate

If fixed costs increase, but variable cost and price remain the same, the break-even point:

increases

If the price decreases, but fixed and variable costs do not change, the break-even point:

increases.

In a network flow model, a directed branch

is a branch in which flow is possible in only one direction.

A slack variable:

is the amount by which the left side of a ≤ constraint is smaller than the right side.

In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit.

media selection

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z* This linear programming problem is a(n):

minimization problem

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a(n) ________ constraint.

mutually exclusive

Simulation does not usually provide recommended decisions. Instead it provides:

operating characteristics

In the Monte Carlo process, values for a random variable are generated by ________ a probability distribution

sampling from

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the

shortest route solution technique.

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is

sometimes optimal and feasible

A shadow price reflects which of the following in a maximization problem?

the marginal gain in the objective that would be realized by adding one unit of a resource

Compared to blending and product mix problems, transportation problems are unique because:

the solution values are always integers

In a ________ integer model, all decision variables have integer solution values.

total

A ________ is a gradual, long-term, up-or-down movement of demand.

trend

Parameters are known, constant values that are usually coefficients of variables in equations

true

In an integer program, if we were choosing between two locations to build a facility, this would be written as:

x1 + x2 = 1

In an integer program, if we were choosing between two locations to build a facility, this would be written as: ________.

x1 + x2 = 1

Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? x1 = 2, x2 = 6, Z = 46 x1 = 3, x2 = 6, Z = 51 x1 = 6, x2 = 4, Z = 54 x1 = 4, x2 = 6, Z = 56

x1 = 4, x2 = 6, Z = 56

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) Which of these is an appropriate constraint for this scenario?

500N + 250R + 125T + 15F ≤ 3,500

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Which of these is not an element of the objective function?

600D

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. Which of the following is not a feasible production combination?

75R and 90D

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. What is the appropriate constraint for the budget?

900 Bar + 1500 Food + 5,000 Excursion ≤ 150,000

A balanced transportation model should have ________ constraints.

= or "equal to"

Binary variables are: A) 0 or 1 only. B) any integer value. C) any continuous value. D) any negative integer value.

A

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem. A) always B) sometimes C) optimally D) never

A

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

A

In a ________ integer model, all decision variables have integer solution values. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

A

Let: rj = regular production quantity for period j, oj = overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is: A) rj + oj + i2 - i1 ≥ dj. B) rj + oj + i1 - i2 ≥ dj. C) rj + oj + i1 - i2 ≤ dj. D) rj - oj - i1 + i2 ≥ dj.

A

Which of the constraints best describes the relationship between the iPads for everyone and the speaker series? A - C = 0 A + C = 2 A + C = 1 A - C ≤ 1

A + C = 1

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Which of these constraints allows for some inventory to be held at one of the crossdock facilities?

AD + BD + CD - DF - DG - DH ≥ 0

Types of integer programming models are: total. 0-1. mixed. all of the above

All of the above

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem. optimally always never sometimes

Always

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected. A) exactly 1, 2 B) exactly 2, 4 C) at least 2, 4 D) at most 1, 2

B

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always feasible. D) never optimal and feasible

B

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

B

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. A) must always B) can sometimes C) can never D) is already

B

In a ________ integer model, the solution values of the decision variables are 0 or 1. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

B

In a multiperiod scheduling problem, the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory. B) beginning inventory - demand + production = ending inventory. C) beginning inventory - ending inventory + demand = production. D) beginning inventory + demand + production = ending inventory.

B

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is: A) 0. B) 1. C) 0 or 1. D) none of the above

B

The type of linear program that compares services to indicate which one is less productive or inefficient is called: A) product mix. B) data envelopment analysis. C) marketing. D) blending.

B

Which constraint best describes the situation with decision variables A and B? B - A = 0 B + A = 1 B - A ≤ 0 B + A ≤ 1

B - A = 0

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

B = 150, M = 0

________ types of linear programming problems often result in fractional relations between variables which must be eliminated.

Blending

A systematic approach to model formulation is to first: A) construct the objective function. B) develop each constraint separately. C) define decision variables. D) determine the right hand side of each constraint.

C

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2." The constraint for this requirement can be written as: A) x2 ≥ .60. B) x2 ≥ .60 (x2 + x7 + x8). C) .4x2 - .6x7 - .6x8 ≤ 0. D) .4x2 - .6x7 - .6x8 ≥ 0.

C

Balanced transportation problems have which of the following type of constraints? A) ≥ B) ≤ C) = D) <

C

For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type. A) up and down B) up C) down D) up or down

C

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

C

In a ________ integer model, some solution values for decision variables are integers and others can be non-integer. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

C

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? A) x1 + x2 + x5 ≤ 1 B) x1 + x2 + x5 ≥ 1 C) x1 + x5 ≤ 1, x2 + x5 ≤ 1 D) x1 - x5 ≤ 1, x2 - x5 ≤ 1

C

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? A) X2 ≤ 10000, X2 + X3 ≤ 350 B) 10,000 X2 ≤ 350X2 + 350X3 C) 47.25X2 ≤ 10,000, X2 + X3 ≤ 350 D) 47.25X2 ≤ 10,000, 47.25 X2 + 110X3 ≤ 350

C

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1. A) x21 + x22 ≤ 8000 B) x12 + x22 ≥ 8000 C) x11 + x12 ≤ 8000 D) x21 + x22 ≥ 8000

C

Max Z = 13x1 + 8x2 Subject to: 15x1 + 12x2 ≤ 144 7x1 + 9x2 ≤ 64 x1, x2 ≥ 0 and integer What is the optimal solution? A) x1 = 5, x2 = 6, Z = 113 B) x1 = 7, x2 = 7, Z = 147 C) x1 = 9, x2 = 0, Z = 117 D) x1 = 0, x2 = 15, Z = 120

C

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. Here's a lovely portion of the sensitivity report for the constraints. Which of these conclusions is reasonable?

Captain Stubing should exhaust his Budget.

is the percentage of the variation in the dependent variable that results from the independent variable.

Coefficient of determination

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. multiple-choice mutually exclusive conditional corequisite

Corequisite

is a measure of the strength of the relationship between independent variable(s) and a dependent variable.

Correlation

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. A) always, optimal B) always, non-optimal C) never, non-optimal D) sometimes, optimal

D

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

D

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. A) can also B) can sometimes C) can never D) must also

D

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. A) x11 + x12 (.35)(x11 + x21) B) x11 + .35(x11 + x12) C) -.65x11 + .35x21 ≤ 0 D) .65x11 - .35x21 ≤ 0

D

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1. A) x21 + x22 = 11000 B) x12 + x22 = 11000 C) x11 + x21 ≤ 11000 D) x11+ x21= 11000

D

Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-base paint, and y represents the gallons of water-base paint, which constraint correctly represents the constraint on ingredient A? A) .9A + .1B ≤ 10,000 B) .9x + .1y ≤ 10,000 C) .3x + .7y ≤ 10,000 D) .9x + .3y ≤ 10,000

D

Which of the following is not an integer linear programming problem? A) pure integer B) mixed integer C) 0-1 integer D) continuous

D

Yowzah receives bids from four companies we'll call A, B, C, and D to supply product for the coming year. Renee DeCartes, the Yowzah VP of Plotting takes the bids and creates this graph to bring to the next executive meeting. The company with the lowest variable cost is:

D

he department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. David is qualified to teach Management Science, but has misplaced his slide rule and doesn't feel he can complete the necessary calculations if he is assigned to teach it next semester. Which of these constraints would ensure that he isn't the instructor?

DM = 0

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Copied below is a portion of the answer report that shows the status of the variable cells related to the faculty assignment. Which of these statements is consistent with the answer report?

David is assigned to teach Introduction to Operations

The ________ is a procedure for developing a consensus forecast about what will occur in the future.

Delphi method

Which constraint is most appropriate if the students can choose only three of these activities?

E + S +L + B ≤ 3

T/F: A conditional constraint specifies the conditions under which variables are integers or real variables.

F

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint.

F

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

F

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

F

T/F: In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected.

F

T/F: In a mixed integer model, all decision variables have integer solution values.

F

T/F: In a mixed integer model, the solution values of the decision variables are 0 or 1.

F

T/F: In the classic game showPassword, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.

F

T/F: Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

F

T/F: The branch and bound solution method cannot be applied to 0-1 integer programming problems.

F

T/F: The management scientist's fiance informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint.

F

A conservative approach to a balanced transportation model would be to make all constraints less-than-or-equal-to constraints. True or False

FALSE

A data envelopment analysis with an objective function value of 0.8 means the company is more efficient than its competitors since it expends only 80% of the effort to achieve the same results. True or False

FALSE

A linear programming model of a media selection problem is used to determine the relative value of each advertising media. True or False

FALSE

Data envelopment analysis indicates which type of service unit makes the highest profit. True or False

FALSE

Diet problems usually maximize nutritional value. True or False

FALSE

Double-subscripted variables are required when there are two decision variables. True or False

FALSE

Fractional relationships among variables are considered standard form in a blending problem. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint. True or False

FALSE

In Excel, a binary constraint in cell A1 is created using the =BIN($A$1) formula. True or False

FALSE

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. True or False

FALSE

In a classic blending problem, revenue is maximized by subtracting cost from profit. True or False

FALSE

In a mixed integer model, all decision variables have integer solution values. True or False

FALSE

In a mixed integer model, the solution values of the decision variables are 0 or 1. True or False

FALSE

In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). True or False

FALSE

In an unbalanced transportation model, supply does not equal demand, and supply constraints must have ≤ signs. True or False

FALSE

In most media selection decisions, the objective of the decision maker is to minimize cost. True or False

FALSE

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate. True or False

FALSE

Product mix problems cannot have greater-than-or-equal-to (≥) constraints. True or False

FALSE

The branch and bound solution method cannot be applied to 0-1 integer programming problems. True or False

FALSE

The constraint x + y = z is written in standard form. True or False

FALSE

The management scientist's fiancé informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint. True or False

FALSE

Transportation problems can have solution values that are non-integer and must be rounded. True or False

FALSE

When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content. True or False

FALSE

When using a linear programming model to solve the diet problem, the objective is generally to maximize profit. True or False

FALSE

A conditional constraint specifies the conditions under which variables are integers or real variables.

False

Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

False

The branch and bound solution method cannot be applied to 0-1 integer programming problems.

False

The term big data refers to numbers of large magnitude, i.e., greater than or equal to one billion.

False

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) Which of these statements about the sensitivity report for the constraints is best?

For every $1 increase in the budget, the ad campaign can reach twelve more customers.

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. Which of these routes for the horse is actually the shortest between the pair of nodes?

Grass - Pond = 190'

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) How should the entry for the Newspaper decision variable be interpreted?

If the director were forced to purchase a newspaper advertisement, he would reach 1000 fewer customers than would be reached using the optimal advertising campaign

Use the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) to represent the decision variables. What of these sets of constraints appropriately limits the number of excursions based on the scenario?

JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1

moving averages react more slowly to recent demand changes than do ________ moving averages

Longer-period, shorter-period

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function?

MAX $3R + $2D

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. The landlord uses the following scheme for decision variables: What should the objective function be?

Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. What should Captain Stubing's objective function be?

Max Z = 1500 Bar + 5000 Food + 17000 Excursion

Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $250 for the excursions&8211;the prices shown are per couple, so for example, the $60 will pay for both of them to fill up on jerk chicken and mannish water. For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3. (Note - data used in this test question should not be construed as vacation advice.) What is an appropriate objective function for this vacation?

Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

What is an appropriate objective function for this vacation? Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu Max Z = JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu Min Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) What is an appropriate objective function for this scenario?

Max Z = 5,000N + 3,000R + 700T + 200F

In all the excitement of waving to the longshoremen as the ship leaves the Port of New Orleans, the management scientist drops his wallet in the Mississippi River. Rather than maximize enjoyment for the three excursions, he must now adjust his model to select three inexpensive options. Which combinations of objective function and constraints are best if the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) is used to represent the decision variables?

Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1

A ________ integer model allows for the possibility that some decision variables are not integers.

Mixed

In a ________ linear programming model, some of the solution values for the decision variables are required to assume integer values and others can be integer or noninteger.

Mixed Integer

________ involves determining the functional relationship between variables, parameters, and equations.

Model construction

is a technique for selecting numbers randomly from a probability distribution.

Monte Carlo

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. MAX 2.5B + 1.5E + 2R s.t. The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia's available hours for paint and seal have fallen from 80 hours to 60 hours because of other commitments. How will this affect her profits?

Profits will not change

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?

R = 90, D = 75, Z = $420

Assuming that Si is a binary variable, the constraint for the first restriction is: S1 + S3 + S7 ≤1. S1 + S3 + S7 = 2. S1 + S3 + S7 ≥ 1. S1 + S3 + S7 ≤ 2.

S1 + S3 + S7 ≤ 2.

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Which constraint ensures that Introduction to Operations is offered according to the scenario?

SI + GI + TI + DI ≥ 6

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Which constraint is appropriate for this scenario?

SI + SP + SQ + SC + SL + SM ≤ 3

When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed.

SUMPRODUCT

T/F: A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.

T

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

T

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.

T

T/F: In a 0-1 integer model, the solution values of the decision variables are 0 or 1.

T

T/F: In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

T

T/F: In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.

T

T/F: In a total integer model, all decision variables have integer solution values.

T

T/F: One type of constraint in an integer program is a multiple-choice constraint.

T

T/F: Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem.

T

T/F: The college dean is deciding among three equally qualified candidates for his associate dean position. If this situation can be modeled as an integer program, the decision variables would be cast as 0-1 integer variables.

T

T/F: The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

T

T/F: The three types of integer programming models are total, 0-01, and mixed.

T

A company can use regular time, overtime, and subcontracting in any amount over the one-year production planning horizon to meet forecasted demand. If they develop the plan using linear programming, they will have a total of 36 decision variables that govern the amount produced by these three methods. True or False

TRUE

A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values. True or False

TRUE

Blending problems usually require algebraic manipulation in order to write the LP in "standard form." True or False

TRUE

Data envelopment analysis problems are usually maximization problems. True or False

TRUE

Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. True or False

TRUE

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint. True or False

TRUE

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint. True or False

TRUE

In a 0-1 integer model, the solution values of the decision variables are 0 or 1. True or False

TRUE

In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. True or False

TRUE

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally, the objective is to maximize the audience exposure. True or False

TRUE

In a mixed integer model, some solution values for decision variables are integer and others can be non-integer. True False

TRUE

In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. True or False

TRUE

In a total integer model, all decision variables have integer solution values. True or False

TRUE

In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). True or False

TRUE

In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill). True or False

TRUE

Integer constraints are entered in the inequality dialog box within Excel's Solver routine. True or False

TRUE

One type of constraint in an integer program is a multiple-choice constraint. True or False

TRUE

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. True or False

TRUE

The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables. True or False

TRUE

The divisibility assumption is violated by integer programming. True or False

TRUE

The feasible region in an integer programming graph is composed of a lattice of points. True or False

TRUE

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several unsold half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible. True or False

TRUE

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct?

The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900.

The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct? The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900. The rent will be $195 higher and the project will take 3.5 weeks to finish at a cost of $3700. The rent will be $180 higher and the project will take 2.5 weeks to finish at a cost of $3700. The rent will be $195 higher and the project will take 2.5 weeks to finish at a cost of $2900.

The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900.

In a ________ integer model, all decision variables have integer solution values. total 0-1 mixed all of the above

Total

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected.

True

In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

True

The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables.

True

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

True

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region. The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4. Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3. The constraint for distribution center 1 is:

X11 + X12 + X13 + X14 - 500y1 ≤ 0

The constraint for distribution center 1 is: X11 + X12 + X13 + X14 ≤ 500. X11 + X12 + X13 + X14 ≥ 500. X11 + X12 + X13 + X14D + 500y1 ≤ 0. X11 + X12 + X13 + X14 - 500y1 ≤ 0.

X11 + X12 + X13 + X14 - 500y1 ≤ 0.

The constraint for the North American supply region is:

X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0

Which of the following could be a linear programming objective function?

Z = 1A + 2B + 3C + 4D

An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models?

additivity

In a balanced transportation model where supply equals demand:

all constraints are equalities.

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________.

audience exposure

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. MAX 2.5B + 1.5E + 2R s.t. The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia is planning for next spring, and she is considering making only two products. Based on the results from the linear program, which two products would you recommend that she make?

baskets and rabbits

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: The local cheese vendor offers to sell Taco Loco 200 pounds of cheese for these three products. Taco Loco should:

buy 46 pounds or less of cheese for $1.45 or less.

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. can never must always is already can sometimes

can sometimes

The field of management science:

concentrates on the use of quantitative methods to assist managers in decision making.

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. multiple choice mutually exclusive conditional corequisite

conditional

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a(n) ________ constraint.

conditional

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a(n) ________ constraint."

contingency or mutually exclusive

Which of the following is not an integer linear programming problem?

continuous

A ________ is an up-and-down repetitive movement that repeats itself over a time span of more than 1 year

cyclical pattern

If fixed costs decrease, but variable cost and price remain the same, the break-even point:

decreases

A systematic approach to model formulation is to first:

define decision variables.

In a balanced transportation model, supply equals ________.

demand

Coefficient of determination is the percentage of the variation in the ________ variable that results from the ________ variable

dependent, independent

A technique that assumes certainty in its solution is referred to as:

deterministic.

Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem.

diet

Rounding a noninteger solution ________ to the nearest integer guarantees a feasible, but perhaps suboptimal solution to an integer programming situation.

down

Data envelopment analysis indicates the relative ________ of a service unit compared with others.

efficiency or productivity

A table of random numbers must be

efficiently generated.

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected.

exactly 2, 4

Linear mathematical programming techniques assume that all parameters in the models are:

known with certainty.

In a finite queue, the length of the queue is:

limited.

Random numbers generated by a ________ process instead of a ________ process are pseudorandom numbers

mathematical, physical

The objective function of a diet problem is usually to ________ subject to nutritional requirements.

minimize costs

A(n) ________ integer model allows for the possibility that some decision variables are not integers.

mixed

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a ________ constraint."

mixed or mutually exclusive

A limitation of simulation is that:

model building is costly and time-consuming

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a(n) ________ constraint.

multiple-choice

In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a(n) ________ constraint.

multiple-choice

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. must also can never can also can sometimes

must also

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint

mutually exclusive

In a network modeling problem, the linear programming decision variables are given by

network branches.

A seed value is a(n):

number used to start a stream of random numbers

The steps of the management science process are:

observation, problem definition, model construction, model solution, implementation.

Consider the following maximization problem. The optimal solution:

occurs where x = 0 and y = 2.

Simulations are normally done

on the computer.

In a data envelopment analysis, it is customary to scale input process so that the total value of a unit's inputs equals ________.

one

Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter.

product mix

An important factor to consider in analyzing a queuing system is the

queue discipline

Developing the cumulative probability distribution helps to determine

random number ranges

The arrival rate is the:

rate of arrivals to the service facility.

Investment problems maximize ________.

return on investments

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:

same product mix, different total profit.

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: never optimal and feasible. always feasible. always optimal and feasible. sometimes optimal and feasible.

sometimes optimal and feasible.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem.

sometimes, optimal

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. always, non-optimal never, non-optimal always, optimal sometimes, optimal

sometimes, optimal

The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination.

source, demand

The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

standard form

If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes?

street intersections

In the linear programming formulation of a transportation network

there is one variable for each arc. there is one constraint for each node. the sum of variables corresponding to arcs out of an source node is constrained by the supply at that node. Correct All of these

There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter.

transportation problem

Rounding a noninteger solution ________ to the nearest integer value will likely result in an infeasible solution.

up

Use the constraints given below and determine which of the following points is feasible.

x = 1; y = 4

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? x1 + x2 + x5 ≤ 1 x1 - x5 ≤ 1, x2 - x5 ≤ 1 x1 + x5 ≤ 1, x2 + x5 ≤ 1 x1 + x2 + x5 ≥ 1

x1 + x5 ≤ 1, x2 + x5 ≤ 1

In an integer program, if building one facility required the construction of another type of facility, this would be written as: ________.

x1 = x2

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. The landlord uses the following scheme for decision variables: Which of these constraints would not be appropriate for this scenario?

x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

Which of these constraints would not be appropriate for this scenario? 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 x3 + x4 = 1 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1.

x11 + x12 ≤ 8000

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables?

x3 + x4 ≤ 1

Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? x3 - x4 = 1 x3 - x4 ≤ 1 x3 + x4 ≤ 1 x3 + x4 = 1

x3 + x4 ≤ 1

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. Suppose the landlord really wants the back door to be installed. For too long he has had to cut through the garage and he figures when he retires, this house will be a perfect downsize home for him to move into. How should the constraint for the back door be written if he uses the following scheme for decision variables?

x5 + x6 = 1

Suppose the landlord really wants the back door to be installed. For too long he has had to cut through the garage and he figures when he retires, this house will be a perfect downsize home for him to move into. How should the constraint for the back door be written if he uses the following scheme for decision variables? x5 + x6 ≤ 1 x5 - x6 ≤ 1 x5 - x6 = 1 x5 + x6 = 1

x5 + x6 = 1

Which of these constraints will ensure that a low capacity facility is not built in South America?

y12 + y22 = 0