App. Stat Exam 3

The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Which of these formulations of the budget constraint is correct? Assume that there are 20 students in this semesters MBA class.

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

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

(x1 + x2 = 1)

The following data represents quarterly sales of lawnmowers. YearQuarter 1Quarter 2Quarter 3Quarter 411501401901652160148210175 What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)

.25

The following data represents quarterly sales of lawnmowers. YearQuarter 1Quarter 2Quarter 3Quarter 411501401901652160148210175 What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)

.25

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

0-1

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

1

Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach?

1148

Consider the following demand and forecast. PeriodDemandForecast17102121531820422 If MAD = 2 for the four periods under consideration, what is the forecast for period 4?

22

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 3-period moving average to forecast demand for period 7.

283.33

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: If the forecast for period 5 is equal to 275, use exponential smoothing to compute a forecast for period 7 if α = .40.

286.2

Given forecast errors of 6, 4, 0 and -2, what is the mean absolute deviation?

3

Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach?

3049

Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach?

3462

Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach?

4.29%

Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. Generate a forecast for the year using this technique and then calculate forecast errors using MAD. What is the mean absolute deviation for this forecasting approach?

49.9

Armed only with his fingers, the owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand and the January forecast just to get the ball rolling. His fingers are aching by the time he reaches March and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for April.

497.4

Armed only with his fingers, the owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. Generate a forecast for the year using this technique and then calculate forecast errors using MAD. What is the mean absolute deviation for this forecasting approach?

57.9

Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. His fingers are aching by the time he reaches May and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for June.

583.5

After tallying the receipts for their first year of operation, the owners of the Taco Barn are encouraged. Sales of their artisnal tacos, made from such exotic ingredients as ground beef, cheese, and beans, have been strong and seem to give hope to the coming year. Taco sales by month are shown in the table. MonthSales January474 February485 March501 April588 May579 June673 July594 August679 September608 October699 November732 December732 Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. His fingers are aching by the time he reaches May and he is worried about his ability to stuff tacos during tomorrow's dinner rush. Help him out by finding the forecast for June.

599.3

Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?

62.5

The manager of "Skis 4 U" is preparing a forecast for February of 2010. Demand exhibits both trend and seasonality. The trend equation for monthly demand is y = 4375 + 80t, where t = 1 for January 2009. The seasonal index for February is 1.25. The forecast for February is:

6769

Armed only with his fingers, the owner decides that the safest forecasting approach is a moving average of two periods. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach?

7.67%

Armed only with his fingers, the owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. Generate a forecast for the year using this technique and then calculate forecast errors using MAPD. What is the mean absolute deviation for this forecasting approach?

8.94%

The Exorbitant Course Fees. The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Decision VariableItemCostNoteAiPads for everybody$750/unitMust get a cover if these are purchasedBiPad covers with MBA logo$25/unitNot needed unless we buy iPadsCSpeaker series$15,000Can't afford both this and the iPadsDSubscriptions to the Wall Street Journal$10/unitDon't need if we have the electronic versionESubscriptions to the electronic version of the Wall Street Journal$5/unitWorthless without the iPads Which of the constraints best describes the relationship between the iPads for everyone and the speaker series?

A+C=1

The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Which constraint best describes the situation with decision variables A and B?

B - A = 0

Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help them immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include: Eiffel Tower visit, $40 per student, EParis Sewer spelunking, $20 per student, SHalf day passes to the Louvre, $60 per student, LBon Beret tour, $50 per student, B So much to do and so little time! Which constraint is most appropriate if the students can choose only three of these activities?

E + S + L + B ≤ 3

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 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. 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 = 1CS + CP + CH + CL + CTe = 1GS + GP + GH + GL + GTu = 1

________ indicates a forecast is biased high.

Large - E

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 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. 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

he ________ is the sum of the absolute value of forecasting errors divided by the number of periods in which a forecast was made.

Mean Absolute deviation (MAD)

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 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. 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

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 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. 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 + 95GTusubject to:JS + JP + JH + JL = 1CS + CP + CH + CL + CTe = 1GS + GP + GH + GL + GTu = 1

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. Region DCABCD113322241333223 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 objective function is

Min Z = 3sigmai-1 4sigmaj=1 Ci jXi + 3sigmai-1 Yi

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. Region DCABCD113322241333223 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 objective function is

Min Z = 3signmai-1 4signmaj-1 cijXij + 3signmai-1 y1

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 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 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.

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million. The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility) The constraint for the North American supply region is:

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

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million. The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows: Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4. Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility) Which of these constraints will ensure that a low capacity facility is not built in South America?

Y12 + Y22 = 0

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.

always

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

binary

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 sometimes

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

contingency or mutual exlusive

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

continuous

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

corequisite

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

correlation

________ error is the sum of the forecast errors.

cumulative

A long-term wave in a demand pattern that undulates gracefully over a period of greater than a year is a(n) ________.

cycle

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

cyclical pattern

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

dependent; independent

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

false

Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

false

Correlation measures the strength of relationship between the x and y variables and the closer it is to 1 or -1, the greater the proof that the level of x determines the level of y

false

Correlation measures the strength of relationship between the x and y variables and the closer it is to 1 or -1, the greater the proof that the level of x determines the level of y.

false

Data cannot exhibit both trend and cyclical patterns.

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 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.

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

Qualitative methods are the least common type of forecasting method for the long-term strategic planning process.

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

Seasonal patterns are observed only during the four seasons - winter, spring, summer, and fall.

false

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

false

The dependent variable in linear regression is usually designated as the x variable.

false

________ is the difference between the forecast and actual demand.

forecast error

The closer the value of α is to zero, the ________ will be the dampening or smoothing effect.

greater

________ is a linear regression model relating demand to time.

linear trend

A(n) ________ forecast typically encompass a period longer than one year.

long range

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

________ are good for stable demand with no pronounced behavioral patterns.

moving averages

________ relates demand to two or more independent variables.

multiple regression

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

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

mutually exclusive

Consider the following graph of sales. /\ __/\. / \. /\__ /\ / \/ \/ \/ Which of the following characteristics is exhibited by the data?

none of these

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

o-1 integer

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

qualitative methods

The major types of forecasting methods are ________, ________, and ________.

qualitative techniques, time series analysis and projection, causal models.

You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5.Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is :

s1 + s3 + s7 <= 2

A(n) ________ is an up-and-down repetitive movement within a trend occurring periodically.

seasonal pattern

Longer-period moving averages react more ________ to recent demand changes than do shorter period moving averages.

slowly

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

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

________ has become increasingly crucial to compete in the modern international business environment.

technological forecasting

________ is a category of statistical techniques that uses historical data to predict future behavior.

time series

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

time series

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

total

Types of integer programming models are:

total mixed 0-1

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

trend

Consider the following graph of sales. /\ __/ \________ Which of the following characteristics is exhibited by the data?

trend plus irregular

A seasonal pattern is an up-and-down repetitive movement within a trend occurring periodically.

true

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

true

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

true

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

true

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

true

In a weighted moving average, weights must sum to 1.

true

Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages.

true

Moving averages are good for stable demand with no pronounced behavioral patterns.

true

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

true

Regression is used to relate one variable to one or more variables.

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 Delphi method develops a consensus forecast about what will occur in the future.

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 divisibility assumption is violated by integer programming.

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

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

true

Time series is a category of statistical techniques that uses historical data to predict future behavior.

true

the basic types of forecasting methods include time series, regression, and qualitative methods.

true

Irregular variations exhibit no pattern.

ture

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 + x5 <= 1, x2 + x5 <= 1

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 + x5 ≤ 1, x2 + x5 ≤ 1

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

x1 = 4, x2 = 6, Z = 56

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

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 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. Which of these constraints would not be appropriate for this scenario?

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

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. Region DCABCD113322241333223 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

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million. The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility) The constraint for the South Asia demand region is:

x13 + x23 + x33 + x43 =7

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

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

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million. The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows:Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4.Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility) Which of these constraints will ensure that a low capacity facility is not built in South America?

y12 + y22 =0