# Mat 540 final exam – 100% score

Question 1

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A cycle is an up and down movement in demand that repeats itself in less than 1 year.

[removed]True

[removed]False

5 points

Question 2

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.

[removed]True

[removed]False

5 points

Question 3

In a transshipment problem, items may be transported from destination to destination and from source to source.

[removed]True

[removed]False

5 points

Question 4

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

[removed]True

[removed]False

5 points

Question 5

[removed]True

[removed]False

5 points

Question 6

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.

[removed]True

[removed]False

5 points

Question 7

The probability of observing x
successes in a fixed number of trials is a problem related to

 [removed] the normal distribution [removed] the binomial distribution [removed] conditional probability [removed] the Poisson distribution

5 points

Question 8

Events that cannot occur at the same time in any trial of an experiment are:

 [removed] exhaustive [removed] dependent [removed] independent [removed] mutually exclusive

5 points

Question 9

Using the minimax regret criterion to make a decision, you

 [removed] Construct a table of regrets. Look at the maximum regret for each decision. Select the decision with the smallest maximum regret. [removed] Look at the worst payoff for each possible decision and select the decision with the largest worst payoff [removed] Construct a table of regrets. Look at the minimum regret for each decision. Select the decision with the smallest minimum regret. [removed] Run in circles, scream and shout

5 points

Question 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.

 Alternative Brisk Slow Buy 90 -10 Rent 70 40 Lease 60 55

The conservative (maximin) strategy is:

 [removed] Buy [removed] Rent [removed] Lease [removed] Brisk.

5 points

Question 11

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.

 Alternative Brisk Slow Buy 90 -10 Rent 70 40 Lease 60 55

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

 [removed] 12 [removed] 55 [removed] 57 [removed] 69

5 points

Question 12

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 constraint on money to invest?

 [removed] Max Z = 85B + 75M [removed] 100B + 50M ≤ 25000 [removed] 100B + 50M ≥ 25000 [removed] 100B + 80M = 18000

5 points

Question 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. What is the objective function?

 [removed] Max Z = 75B + 85M [removed] Max Z = 85B + 75M [removed] 100B + 50M ≤ 25000 [removed] 100B + 50M ≥ 25000 [removed] 100B + 80M ≤ 18000 [removed] 100B + 80M ≥ 18000

5 points

Question 14

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?

 [removed] 0 to 4 [removed] 2 to 5.33 [removed] 0 to 5.33 [removed] 4 to 6.33

5 points

Question 15

The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He 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?

 [removed] \$1000 [removed] \$900 [removed] \$800 [removed] \$700

5 points

Question 16

Compared to transportation LP problems, assignment problems are unique because

 [removed] The supply at each source is limited to 1 unit. [removed] The demand at each destination is limited to 1 unit. [removed] Both of the above [removed] None of the above.

5 points

Question 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:

 [removed] .5A + .75B = 20 [removed] .3B = 20 [removed] .3 B≤ 20 [removed] .3B ≥ 20

5 points

Question 18

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

 [removed] multiple choice [removed] mutually exclusive [removed] conditional [removed] corequisite

5 points

Question 19

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?

 [removed] x1 + x2 + x5 ≤ 2 [removed] x1 + x5 ≤ 1, x2 + x5 ≤ 1 [removed] x1 + x2 + x5 ≥1 [removed] x1 – x5 ≤ 1, x2 -–x5 ≤ 1

5 points

Question 20

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

 DC A B C Supply 1 4 6 8 500 2 5 2 7 400 3 3 5 9 300

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

 [removed] 4X1A + 6X1B + 8X1C ≤ 500 [removed] 4X1A + 6X1B + 8X1C = 500 [removed] X1A + X1B + X1C ≤ 500 [removed] X1A + X1B + X1C ≥500

5 points

Question 21

The assignment problem constraint x31+x32+x33+x34 ≤ 2 means

 [removed] agent 3 can be assigned to 2 tasks [removed] agent 3 can be assigned to no more than 2 tasks [removed] a mixture of agents 1, 2, 3 and 4 will be assigned to tasks [removed] agent 2 can be assigned to 3 tasks

5 points

Question 22

Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking lot?

 [removed] 11.13% [removed] 47.72% [removed] 43.32% [removed] 62.47%

5 points

Question 23

Professor Dewey would like to assign grades such that 15% 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.)

 [removed] 75 [removed] 79 [removed] 84 [removed] 88

5 points

Question 24

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

 [removed] 0 [removed] 1 [removed] 2 [removed] 3

5 points

Question 25

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?

 [removed] 36.9 [removed] 57.5 [removed] 60.5 [removed] 62.5

5 points

Question 26

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

 [removed] sampling from [removed] running [removed] integrating [removed] implementing

5 points

Question 27

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

 [removed] Longer-period, shorter-period [removed] Shorter-period, longer-period [removed] Longer-period, longer-period [removed] Shorter-period, shorter-period

5 points

Question 28

Carter’s Bed & Breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is \$1050 per month and the revenue they receive from each booked room is \$150. What is the variable cost per occupied 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).

5 points

Question 29

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).

5 points

Question 30

Suppose that a production process requires a fixed cost of \$50,000. The variable cost per unit is \$10 and the revenue per unit is projected to be \$50. Find the break-even point.

5 points

Question 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

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.

5 points

Question 32

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of \$30 on each tractor and \$30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation:
Let x = number of tractors produced per period
y = number of lawn mowers produced per period
MAX 30x + 30y
subject to 2 x + y ≤ 60
2 x + 3y ≤ 120
x ≤ 45
x, y ≥ 0
The graphical solution is shown below.

What is the shadow price for fabrication? Write your answers with two significant places after the decimal and do not include the dollar “\$” sign.

5 points

Question 33

Klein 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 (%) Partner’s Choice \$0.20 45 20 Feline Excel \$0.15 15 30

Klein 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

5 points

Question 34

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

Max Z = x1 + 6×2
Subject to: 17×1 + 8×2 ≤ 136
3×1 + 4×2 ≤ 36
x1, x2 ≥ 0 and integer

5 points

Question 35

Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3. Find P(x ≤ 6). Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.

5 points

Question 36

Mr. Sartre 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 38 25 33 10 B 10 15 20 85 C 20 100 20 -25 D 25 25 100 25

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

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 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.

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 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.

5 points

Question 39

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

 Month Actual Demand May 19 June 20 July 23 August 21

The forecasted demand for May, June, July and August were 17, 18, 20 and 24 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

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.

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