8. Colonial State College is considering building a new multipurpose athletic complex on campus.  The complex would provide a new gymnasium for intercollegiate basketball games, expanded office space, classrooms, and intramural facilities.  The following activities would have to be undertaken before construction can begin:

Activity Description Intermediate Time

Predecessor (weeks)

A Survey Building site _ 6

B Develop initial design _ 8

C Obtain board approval A, B 12

D Select architect C 4

E Establish budget C 6

F Finalize design D, E 15

G Obtain financing E 12

H Hire contractor F, G 8

1. Draw a project network.
2. Identify the critical path.
3. Develop the activity schedule for the project.
4. Does it appear reasonable that construction of the athletic complex could begin one year after the decision to begin the project with the site survey and initial design plans? What is the expected completion time for the project?

11. Building a backyard swimming pool consists of nine major activities. The activities and their immediate predecessors are shown. Develop the project network.

Activity A B C D E F G H I

Immediate Predecessor _ _ A, B A, B B C D D, F E, G, H

12. Assume that the activity time estimates (in days) for the swimming pool construction project in Problem 11 are as follows:

Activity Optimistic Most Probable Pessimistic

A 3 5 6

B 2 4 6

C 5 6 7

D 7 9 10

E 2 4 6

F 1 2 3

G 5 8 10

H 6 8 10

I 3 4 5

1. What are the critical activities?
2. What is the expected time to complete the project?
3. What is the probability that the project can be completed in 25 or fewer days?

21. Consider the following project network and activity times (in days):

Activity A B C D E F G

Time 3 2 5 5 6 2 2

The crashing data for this project are as follows:

Time (days) Cost ($)

Activity Normal Crash Normal Crash

A 3 2 800 1400

B 2 1 1200 1900

C 5 3 2000 2800

D 5 3 1500 2300

E 6 4 1800 2800

F 2 1 600 1000

G 2 1 500 1000

1. Find the critical path and the expected project completion time.
2. What is the total project cost using the normal lines?

Chapter 2 An Introduction to Linear Programming (Problem 28)

2. Find the solutions that satisfy the following contraints:

1. 4 A + 2 B ≤ 16
2. 4 A + 2 B ≥ 16
3. 4 A + 2 B = 16

6. Refer to the computer solution of the Kelson Sporting Equipment problem in Figure 3.13 (see Problem 5)

1. Determine the objective coefficient ranges.
2. Interpret the ranges in part (a)
3. Interpret the right-hand-side ranges.
4. How much will the value of the optimal solution improve if 20 extra hours of packaging and shipping time are made available?

13. Refer to the computer solution of Problem 12 in Figure 3.17.

1. Identify the range of optimality for each objective function coefficient.
2. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be?
3. Identify the range of feasibility for the right-hand-side values.
4. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.

20. Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

1. Formulate a liner programming model that can be used to determine the amount of funds ASB should allocate to each type of loan in order to maximize the total annual return for the new funds.
2. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return?
3. If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan change? Explain.
4. Suppose the total amount of new funds available was increased by $10,000. What effect would this have on the total annual return? Explain.
5. Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change?

29. La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine , a rose wine, and fruit juice. To meet taste specifications, the wine cooler must consist of at least 50% white wine, at least 20% and no more than 30% rose, and exactly 20% fruit juice. La Jolla purchases the wine from local wineries and the fruit juice from a processing plant in San Francisco. For the current production period, 10,000 gallons of white wine and 8000 gallons of rose wine can be purchased; and unlimited amount of fruit juice can be ordered. The costs for the wine are $1.00 per gallon for the white and $1.50 per gallon for the rose; the fruit juice can be purchased for $0.50 per gallon. La Jolla Beverage Products can sell all of the wine cooler they can produce for $2.50 per gallon.

1. Is the cost of the wine and fruit juice a sunk cost or a relevant cost in this situation? Explain.
2. Formulate a linear program to determine the blend of the three ingredients that will maximize the total profit contribution. Solve the linear program to determine the number of gallons of each ingredient La Jolla should purchase and the total profit contribution they will realize from this blend.
3. If La Jolla could obtain additional amounts of the white wine, should they do so? If so, how much should they be willing to pay for each additional gallon, and how many additional gallons would they want to purchase?
4. If La Jolla Beverage Products could obtain additional amounts of the rose wine, should they do so? If so, how much should they be willing to pay for each additional gallon, and how many additional gallons would they want to purchase?
5. Interpret the dual value for the constraint corresponding to the requirement that the wine cooler must contain at least 50% white wine. What is your advice to management given this dual value?
6. Interpret the dual value for the constraint corresponding to the requirement that the wine cooler must contain exactly 20% fruit juice. What is your advice to management given this dual value?

Chapter 4 Linear Programming Applications in Marketing, Finance, and Operations Management (Problem 25 & Case Problem 1)

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