# Mat 540 final exam – 100% correct answers

Question 1

In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.

5 points

Question 2

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

5 points

Question 3

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

5 points

Question 4

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

5 points

Question 5

Fractional relationships between variables are not permitted in the standard form of a linear program.

5 points

Question 6

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

5 points

Question 7

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

5 points

Question 8

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.

5 points

Question 9

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.

The conservative (maximin) strategy is: Answer

Rent

Lease

Brisk.

5 points

Question 10

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

exhaustive

dependent

independent

mutually exclusive

5 points

Question 11

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

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. 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 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 storage space constraint? Answer

Max Z = 75B + 85M

100B + 50M ≥ 25000

100B + 80M ≤ 18000

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? Answer

0 to 4

2 to 5.33

0 to 5.33

4 to 6.33

5 points

Question 15

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

The Sensitivity Report:

mix/mold

kiln

paint and seal

Cannot tell from the information provided

5 points

Question 16

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

5 points

Question 17

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. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? Answer

X1 ≤ 0.35

X1 = 0.35 (50000)

X1 ≤ 0.35(X1 + X2 + X3)

X1 = 0.35(X1 + X2 + X3)

5 points

Question 18

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

multiple choice

mutually exclusive

conditional

corequisite

5 points

Question 19

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 the constraint that indicates they have to use at least three of the five machines in their production. Answer

Y1 + Y2 + Y3 + Y4 + Y5 ≤ 3

Y1 + Y2 + Y3 + Y4 + Y5 = 3

Y1 + Y2 + Y3 + Y4 + Y5 ≥ 3

none of the above

5 points

Question 20

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

agent 3 can be assigned to 2 tasks

agent 3 can be assigned to no more than 2 tasks

a mixture of agents 1, 2, 3 and 4 will be assigned to tasks

agent 2 can be assigned to 3 tasks

5 points

Question 21

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 5 points

Question 22

Jack 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. The decisions of each university have no effect on each other. This means that they are: Answer

mutually exclusive

independent

controlled by the central limit theorem

all of the above

5 points

Question 23

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? Answer

11.13%

47.72%

43.32%

62.47%

5 points

Question 24

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

sampling from

running

integrating

implementing

5 points

Question 25

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

5 points

Question 26

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? Answer

36.9

57.5

60.5

62.5

5 points

Question 27

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

0

1

2

3

5 points

Question 28

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 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

Nixon’s Bed and Breakfast has a fixed cost of \$5000 per month and the revenue they receive from each booked room is \$200. The variable cost per room is \$75. How many rooms do they have to sell each month to break even? (Note: The answer is a whole number. Give the answer as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms).

5 points

Question 31

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 assembly? Write your answers with two significant places after the decimal and do not include the dollar “\$” sign.

5 points

Question 32

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

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 33

Kitty 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 (%)

Meow Munch

\$0.20

30

10

Feline Feed

\$0.15

15

30

Kitty 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

Let us take as a given that x is normally distributed with a mean of 8.5 and a standard deviation of 2, what is 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

The following sales data are available for 2003-2008 :

Year

Sales

Forecast

2003

7

7

2004

8

8.5

2005

12

10.5

2006

14

13

2007

16

15

2008

18

16

Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468

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.