# Mat 540/mat540 week 11 final exam

Question 1 |

X1 = 0.35 (50000) |

X1 ≤ 0.35(X1 + X2 +.X3) |

X1 = 0.35(X1 + X2 +.X3) |

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.

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

Question 18

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?

Answer

x1 + x2 + x5 ≤ 1

x1 + x2 + x5 ≥1

x1 + x5 ≤ 1, x2 + x5 ≤ 1

x1 – x5 ≤ 1, x2 – x5 ≤ 1

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

Question 20

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

(chart would not copy/paste)

The constraint that represents the quantity demanded by Customer B is:

Answer

6X1B + 2X2B + 8X3B ≤ 350

6X1B + 2X2B + 8X3B = 350

X1B + X2B + X3B ≤ 350

X1B + X2B + X3B = 350

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.

(chart would not copy/paste)

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

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?

Answer

11.13%

47.72%

43.32%

62.47%

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.)

Answer

75

79

84

88

Question 24

Consider the following graph of sales.

(graph would not copy/paste)

Which of the following characteristics is exhibited by the data?

Answer

Trend only

Trend plus seasonal

Trend plus irregular

Seasonal

Question 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

Question 26

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

Question 27

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

Answer

sampling from

running

integrating

implementing

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.

Answer

Question 29

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).

Answer

Question 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

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.

(chart would not copy/paste)

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.

(graph would not copy/paste)

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

Answer

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.

(chart would not copy/paste)

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.

(graph would not copy/paste)

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

Answer

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

Answer

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

Answer

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

Question 36

Ms. Hegel 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 80 15 18 47

B 50 75 35 35

C -90 225 -50 12

D 36 25 25 27

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

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.

(chart would not copy/paste)

Answer

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.

(chart would not copy/paste)

Answer

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

Answer

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.

(graph would not copy/paste)

Answer