# MAT540 Final Exam – In a transhipment problem, items may be transported from destination to destination

# MAT 540 Final Exam

• Question 1

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

• Question 2

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

• Question 3

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

• Question 4

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

• Question 5

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

• Question 6

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

• Question 7

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

• Question 8

Using the maximin criterion to make a decision, you

• Question 9

Using the minimax regret criterion to make a decision, you

• 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.

The conservative (maximin) strategy is:

• Question 11

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

• 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?

• 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?

• Question 14

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

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?

• Question 16

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

• 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

• Question 18

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

• 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.

• Question 20

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

• Question 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 demanded by Customer B is:

• 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?

• Question 23

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:

• Question 24

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

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

• 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?

• Question 27

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

• Question 28

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 29

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 30

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).

• 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.

• 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 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.

• Question 33

Kalamazoo 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

• 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

• 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.

• 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

• 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.

• 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.

• 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

• 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.