staty

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25.The LP formulation that maximizes week profit shown below.MAX 15A +18B + 25 Cs.t.2A + 2.5B + 3C ≤ 30020A + 30B + 45C ≤ 375010A + 14B + 18C ≤ 3000The solution from QM for Windows is show below.Billy's accountant made an error, and the budget has been reduced from $3000 to $2500. Billy's profit will go down by:

$0

What is the equation for the constraint AB?

12X +3Y ≥ 36

Line segment GH represents the objective function. Which constraint has surplus?

AB

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

alternate optimality

What is the equation for constraint EF?

4X + 8Y ≥ 64

For the constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y ≤ 42 (2) x + 3y ≥ 6

x = 1; y = 2

In a linear programming problem, a valid objective function can be represented as:

Max 3x + 3y + 1/3 z

Which of the following statements is not true?

An infeasible solution violates all constraints.

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 line is represented by the equation 2X + Y ≥ 8?

BF

AtwitterThe 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...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? Fina -1000500010001E+30

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

Which of the following is not a typical characteristic of a linear programming problem?

The problem can be solved graphically

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

beginning inventory - demand + production = ending inventory.

Multiple optimal solutions provide ________ flexibility to the decision maker.

greater

In order for an optimization problem to have multiple optimal solutions

the objective function and one constraint must have the same slope

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. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: 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

Given the following linear program that maximizes revenue:Max Z = 15x + 20ys.t.8x + 5y ≤ 404x + y ≥ 4What is the maximum revenue at the optimal solution?

$160

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:

.4x2 - .6x7 - .6x8 ≤ 0

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.An appropriate part of the model would be

15X1 + 47.25X2 + 110 X3 ≤ 50,000

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 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

Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas.A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. What is an appropriate constraint for this fast food vignette?

2N + 4B + 4Q + 3E ≤ 400

Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas.A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. How many decision variables are in the LP formulation?

4

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

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. ;... 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

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 line is represented by the equation 2X + Y ≥ 8?

BF

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. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia can obtain an additional 10 hours of kiln capacity free of charge from a friend. If she did this, how would her profits be affected?

Cannot tell from the information provided

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*

DH

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 constraints has a surplus greater than 0?

DH

AtwitterThe 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,"...During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.)What is the proper interpretation of the shadow price for Facebook?

Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. ... Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. Which of the following is an appropriate objective function?

Max Z = 5L + 2C + 4.5B

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. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. Suppose the charitable organization contacted Aunt Anastasia and told her that they had underestimated the amount of rabbits they needed. Instead of 25 rabbits, they need 35. How would this affect Aunt Anastasia's profits?

Profits would decrease by $5

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

______ is used to analyze changes in model parameters.

Sensitivity analysis

_______ is used to analyze changes in model parameters

Sensitivity analysis

Using this snippet of the sensitivity report for constraints, which of these conclusions is best? FinalShadowConstraintAllowableAllowable CellNameValuePriceR.H. SideIncrease Decrease$E$ 15One451451. 66666666745$E$16Two5 40561E+302$E$17Three 270671E+3040$E$18 Four720781E+306

Taking away four units of One will lower the objective function value by four.

Spring is right around the corner and that can mean only one thing: i...Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. Use this portion of the sensitivity report to evaluate the following statements:

The noise level around the farm should be over 60 decibels.

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

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

A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 300 minutes, providing two additional machine hours will result in:

a different product mix, different total profit

How would multiple optimal solutions typically appear on a graphical solution?

a line

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:Max 2T + 3S + 4STs.t 3T + 6S ≤ 40 10T + 10S ≤ 66 10T + 15S ≤ 99 His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models?

additivity

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. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 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.Max R = 14Z + 13Y + 17Xsubject to:Beef 2Z + 3Y + 4X ≤ 28Cheese 9Z + 8Y + 11X ≤ 80Beans 4Z + 4Y + 2X ≤ 68X,Y,Z ≥ 0The 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

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*.

has no surplus

For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________

improvement, resource

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25.The LP formulation that maximizes week profit shown below.MAX 15A +18B + 25 Cs.t.2A + 2.5B + 3C ≤ 30020A + 30B + 45C ≤ 375010A + 14B + 18C ≤ 3000The solution from QM for Windows is show below.If Billy could acquire more of any resource, which would it be?

machining time

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. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

only time

An optimization problem that has multiple optimal solutions:

provides the decision-maker with increased flexibility.

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

rj + oj + i2 - i1 ≥ dj

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

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

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.If the production manager decides to produce of 400 bottles of light beer and 0 bottles of dark beer, it will result in slack of:

wheat only

Use the constraints given below and determine which of the following points is feasible. (1) 14x + 6y ≤ 42(2) x - y ≤ 3

x = 1; y = 4

What combination of x and y is a feasible solution that minimizes the value of the objective function? Min Z = 3x + 15y (1) 2x + 4y ≥ 12 (2) 5x + 2y ≥10

x = 5; y = 0