1. Jack Buys hot dogs each morning for his stand in the city. Jack prides himself on slow-roasted,

always fresh hot dogs. As a result, he will sell only hot dogs purchased that morning. Each hot dog

plus bun and condiments sell for $1.50 and costs Jack $0.67. Assume Jack can purchase any number

of hot dogs. Because tomorrow is Friday, Jack knows tomorrow’s hot dog demand will be normally

distributed with mean 375 hot dogs and variance 400. If Jack has any hot dogs left over, he either

eats them or gives them away to less fortunes, earning no additional revenue. If Jack wants to

maximize his profits, how many hot dogs should he purchase? How many hot dogs should he buy if

leftover hot dogs could always be sold for $0.50?

2. Sam Crawford, a junior business major, lives off campus and has just missed the bust that would

have taken him to campus for his 9:00 AM test. It is now 8:45 AM and Sam has several options

available to get him to campus: waiting for the next bus, walking, riding his bike, or driving his car.

The bus is scheduled to arrive in 10 minutes, and it will take Sam exactly 20 minutes to get to his test

form the time he gets on the bus. However, there is 0.2 chance that the bus will be 5 minutes early,

0.3 chance that the bus will be 5 minutes late. If Sam walks, there is a 0.8 chance he will get to his

test in 30 minutes, and a 0.2 chance he will get there in 35 minutes. If Sam rides his bike, he will get

to the test in 25 minutes with probability 0.5, 30 minutes with probability 0.4, and there is 0.1

chance of a flat tire, causing him to take 45 minutes. If Sam drives his car to campus, he will take 15

minutes to get to campus, but the time needed to park his car and get to his test is given by the

following table:

Time to park and arrive (minutes)

10 15 20 25

Probability 0.30 0.45 0.15 0.10

Assuming that Sam wants to minimize his expected late time in getting to his test, draw a decision

tree and determine his best option.

3. Benson Electronics manufactures three components used to produce cellular telephones and other

communication devices. In a given production period, demand for the three components may

exceed Benson’s manufacturing capacity. In this case, the company meets demand by purchasing

the components from another manufacturer at an increased cost per unit. Benson’s manufacturing

cost per unit and purchasing cost per unit for the three components are as follows:

Source Component 1 Component 2 Component 3

Manufacture $4.50 $5.00 $2.75

Purchase $6.50 $8.80 $7.00

Manufacturing times in minutes per unit for Benson’s three department are as follows:

Department Component 1 Component 2 Component 3

Production 2 3 4

Assembly 1 1.5 3

Testing and Packaging 1.5 2 5

For the next production period, Benson has capacities of 360 hours in the production department, 250

hours in the assembly department, and 300 hours in the testing and packaging department.

A. Formulate a LP model that can be used to determine how many units of each component to

manufacture and how many units of each component to purchase. Assume that components

demands that must be satisfied are 6000 units for component 1, 4000 units for component 2

and 3500 for component 3. The objective is to minimize the total manufacturing and purchasing

cost.

B. What are the optimal units of components to manufacturing and purchasing?

C. Which departments are limiting Benson’s manufacturing quantities? Use the dual price to

determine the value of an extra hour in each of these departments.

D. Suppose that Benson had to obtain on additional unit of component 2. Discuss what the dual

price for the component 2 constraint tells us about the cost to obtain the additional unit.

4. A project has for activities (A,B,C, and D) that must be performed sequentially. The probability

distribution for the time required to complete each of the activities are as follows:

Use the random numbers 0.1778, 0.9617, 0.6849, and 0.4503 to simulate the completion time of the

project in weeks.

Activity Activity Time (weeks) Probability

A

5 0.25

6 0.35

7 0.25

8 0.15

B

3 0.20

5 0.55

7 0.25

C

10 0.10

12 0.25

14 0.40

16 0.20

18 0.05

D 8 0.60

10 0.40