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

Answer True False 2.In a transshipment problem, items may be transported from destination to destination and from source to source.

Answer True False 3.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.

Answer True False 4. Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality. Answer True False 5. If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

Answer True False

6. Validation of a simulation model occurs when the true steady state average results have been reached.

Answer True False 7. In linear programming problems, multiple optimal solutions occur Answer

when constraint lines are parallel to each other.

when the objective function is parallel to a constraint line

every possible solution point violates at least one constraint

when the dual price for a particular resource is very small

8. Using the maximin criterion to make a decision, you Answer

Construct a table of regrets. Look at the maximum regret for each decision. Select the decision with the smallest maximum regret.

Look at the worst payoff for each possible decision and select the decision with the largest worst payoff

Look at the best payoff for each possible decision and select the decision with the largest best payoff

Consult an astrological table to forecast the state of nature 9. In a break-even model, if all of the costs are held constant, how does an increase in price affect the model? Answer

Breakeven point decreases

Breakeven point increases

Breakeven point does not change

The revenue per unit goes down 10. A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: Answer

12

55

57

69

11. If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: Answer

12

55

57

69

12. An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________. Answer

a decision variable.

a parameter.

an objective function.

a constraint.

13. Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased? Answer

B = 225, M = 0

B = 0, M = 225

B = 150, M = 75

B = 75, M = 150 14. Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint? Answer

Max Z = 75B + 85M

100B + 50M ? 25000

100B + 80M ? 18000

100B + 80M = 18000 15 Given the following linear programming problem that minimizes cost. Min Z = 2x + 8y Subject to 8x + 4y ? 64 2x + 4y ? 32 y ? 2

What is the sensitivity range for the third constraint, y ? 2? Answer

0 to 4

2 to 5.33

0 to 5.33

4 to 6.33

16. The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:

The Answer Report:

The Sensitivity Report:

Which additional resources would you recommend to be increased? Answer

mix/mold

kiln

paint and seal

Cannot tell from the information provided

17. The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40

The constraint for ingredient 3 is: Answer

.5A + .75B = 20

.3B = 20

.3 B? 20

.3B ? 20 18… In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 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 Answer

15X1 + 47.25X2 +110 X3 ? 50,000

MAX Z =15X1 + 47.25X2 + 110X3

X1 + X2 +X3 ? 50,000

MAX Z = 50(15)X1 + 50 (47.25)X2 + 50 (110)X3

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

multiple choice

mutually exclusive

conditional

corequisite

20. The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. Answer

Y1 + Y4 ? 0

Y1 + Y4 = 0

Y1 + Y4 ? 1

Y1 + Y4 ? 1

21 The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.

The constraint that represents the quantity supplied by DC 1 is: Answer

4X1A + 6X1B + 8X1C ? 500

4X1A + 6X1B + 8X1C = 500

X1A + X1B + X1C ? 500

X1A + X1B + X1C ?500

22. A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.

Which of the following constraints represents the assignment for student A? Answer

XA1 +XA2 + XA3 + XA4 = 0

XA1 +XA2 + XA3 + XA4 = 1

XA1 +XA2 + XA3 + XA4 ? 1

XA1 +XA2 + XA3 + XA4 ? 0 23. The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Note: please provide your answer to 2 places past the decimal point, rounding as appropriate. Answer

0.03

0.05

0.07

0.09

24. Professor Truman would like to assign grades such that 10% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.) Answer

75

79

84

88

25. Consider the following graph of sales.

Which of the following characteristics is exhibited by the data? Answer

Trend only

Trend plus seasonal

Trend plus irregular

Seasonal

25. For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:

Answer

0

1

2

3

27. 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 ten-minute intervals, the following probability distribution and random number assignments developed.

Number of Arrivals Probability Random numbers 6 .1 .01 – .10 7 .3 .11 – .40 8 .3 .41 – .70 9 .2 .71 – .90 10 .1 .91 – .00

Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period? Answer

23

24

22

25

__________ moving averages react more slowly to recent demand changes than do __________ moving averages. Answer

Longer-period, shorter-period

Shorter-period, longer-period

Longer-period, longer-period

Shorter-period, shorter-period 28. Ford’s Bed & Breakfast breaks even if they sell 50 rooms each month. They have a fixed cost of $6500 per month. The variable cost per room is $30. For this model to work, what must be the revenue per room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00). Answer

29. Joseph is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. What is the probability that Jim will not be accepted at either university? (Note: write your answer as a probability, with two decimal places. If necessary, round to two decimal places. For instance, a probability of 0.252 should be written as 0.25). Answer

30.

Students are organizing a “Battle of the Bands” contest. They know that at least 100 people will attend. The rental fee for the hall is $200 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? (Note: Write your answer with two significant places after the decimal and do not include the dollar “$” sign. For instance, for five dollars, write your answer as 5.00).

Answer

31. Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX 50R + 75S s.t. 1.2R + 1.6 S ? 600 assembly (hours) 0.8R + 0.5 S ? 300 paint (hours) .16R + 0.4 S ? 100 inspection (hours)

Sensitivity Report:

Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$7 Regular = 291.67 0.00 50 70 20 $C$7 Super = 133.33 0.00 75 50 43.75

Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67 $E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175 $E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40

If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

Answer

32. onsider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX 50R + 75S s.t. 1.2R + 1.6 S ? 600 assembly (hours) 0.8R + 0.5 S ? 300 paint (hours) .16R + 0.4 S ? 100 inspection (hours)

Sensitivity Report:

Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$7 Regular = 291.67 0.00 50 70 20 $C$7 Super = 133.33 0.00 75 50 43.75

Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67 $E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175 $E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40

A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

Answer

33. alamazoo Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:

Cat Food Cost/oz protien (%) fat (%) Pet’s Choice 0.35 40 15 Feline Chow 0.32 20 30

Kalamazoo Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “$” sign. For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45

Answer

34. Question 34

Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.

MAX Z = 5×1 + 8×2 s.t. x1 + x2 ? 6 5×1 + 9×2 ? 45 x1, x2 ? 0 and integer Answer

5 points Question 35

A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan participants are expected to survive to see their 75th birthday? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.

Answer

5 points Question 36

Ms. James is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Investment Economic Conditions Poor (S1) Average (S2) Good (S3) Excellent (S4) A 18 25 50 80 B 19 100 50 75 C 100 26 120 60 D 20 27 50 240

Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable Answer

5 points Question 37

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.

Answer

5 points Question 38

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.

Answer

Question 39

Recent past demand for product ABC is given in the following table.

Month Actual Demand May 33 June 32 July 39 August 37

The forecasted demand for May, June, July and August were 25, 30, 33, and 38 respectively. Determine the value of MAD. Note: Please express the result as a number with 2 decimal places. If necessary, round your result accordingly. For instance, 9.146, should be expressed as 9.15 Answer 5 points

Question 40

Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.

Answer