# Mathematics 540 final exam 2017 march all correct answers

Subject: Mathematics    / General Mathematics
Question

· Question 1

5 out of 5 points

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

· Question 2

5 out of 5 points

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

· Question 3

5 out of 5 points

· Question 4

5 out of 5 points

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

· Question 5

5 out of 5 points

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

· Question 6

5 out of 5 points

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

· Question 7

5 out of 5 points

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:

· Question 8

5 out of 5 points

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

· Question 9

5 out of 5 points

Using the minimax regret criterion to make a decision, you

· Question 10

5 out of 5 points

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:

· Question 11

5 out of 5 points

Using the maximin criterion to make a decision, you

· Question 12

5 out of 5 points

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?

· Question 13

5 out of 5 points

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?

· Question 14

5 out of 5 points

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:

· Question 15

5 out of 5 points

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

The Sensitivity Report:

Which additional resources would you recommend to be increased?

· Question 16

5 out of 5 points

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

· Question 17

5 out of 5 points

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:

· Question 18

5 out of 5 points

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

· Question 19

5 out of 5 points

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.

· Question 20

5 out of 5 points

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

· Question 21

5 out of 5 points

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?

· Question 22

5 out of 5 points

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?

· Question 23

5 out of 5 points

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.)

· Question 24

5 out of 5 points

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?

· Question 25

5 out of 5 points

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

· Question 26

5 out of 5 points

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

· Question 27

5 out of 5 points

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

· Question 28

5 out of 5 points

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).

· Question 29

5 out of 5 points

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).

· Question 30

5 out of 5 points

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).

· Question 31

5 out of 5 points

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

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.

· Question 32

5 out of 5 points

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.

· Question 33

5 out of 5 points

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

· Question 34

5 out of 5 points

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

· Question 35

5 out of 5 points

Let’s say that 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 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75th

· Question 36

5 out of 5 points

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

· Question 37

5 out of 5 points

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.

· Question 38

5 out of 5 points

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.

· Question 39

5 out of 5 points

The following sales data are available for 2003-2008 :

Year

Sales

Forecast

2003

7

9

2004

12

10

2005

14

15

2006

20

22

2007

16

18

2008

25

21

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

· Question 40

5 out of 5 points

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.