Description

Homework 5
(11:30 a.m.)

******************************************************************************************** Note: 1. Your homework submission must be typewritten.

1. Show only the solutions and do not copy the problems in the submission.
********************************************************************************************

1. Read Readings 5 and 6.

Each ITC class requires 15 hours of preparation/instruction time and contributes a profit of $360, whereas each CWP class calls for only 6 hours and contributes $150. Available time for these two courses is limited to 112 hours a day. There is a restriction on the maximum number of trainees that can be efficiently handled. More specifically, at most 50 students can be accommodated on a daily basis without putting a strain on the facility and support staff. Additionally, each course has a class size limit: 3 for ITC and 6 for CWP. HTI would like to maximize the daily total profit from both courses so that it could offer certain other courses on a “goodwill” basis.

Formulate an AILP for management to decide how many classes should be scheduled for each subject daily.

3. The Gorgon Chemical Company in Lancaster, Pa., manufactures and sells an extremely effective termite spray either (1) in a 55-gallon drum for $50 or (2) in bulk form at $1.25 per gallon. It has just received a new shipment of the two chemicals required for the spray and has available several workers to mix the product. The characteristics of the mixing process are summarized below:

Chemical requirement (1) Chemical requirement (2) Chemical availability
(gallons/drum) (gallons/gallon) (gallons)
————————————————————————————————————————————–
Chemical A 33.34 0.88 2,000 Chemical B 26.66 0.50 1,500
————————————————————————————————————————————–

Labor requirement (1) Labor requirement (2) Labor availability
(hours/drum) (hours/gallon) (hours)
————————————————————————————————————————————–
Work force 1.06 0.08 160
————————————————————————————————————————————–

Represent the problem situation by an MILP that can be employed to develop the production plan with the maximum total revenue.

2
FR BR BU BA

GH 55 55 52 54 MS 52 58 53 53 JM 51 54 55 57 CJ 57 55 56 54

(1) Set up a ZOLP for the assignment problem that can be used to determine who should swim which stroke in order to have the best chance to win.

(2) Solve the ZOLP in (1) by running Solver. Be sure to copy and paste the Answer report at the appropriate place in your homework submission. What are the optimal solution and the optimal objective function value? What do they mean here?

Camera location Stadium areas covered
——————————————————–
1 1, 6, 12, 17
2 2, 4, 6, 8
3 20, 22, 24, 25
4 6, 11
5 2, 10, 16, 23
6 18, 21, 24, 25
7 8, 14, 15, 16, 17
8 3, 6, 10, 12, 14
9 1, 2, 18, 19, 21
10 2, 5, 9, 11, 13
11 8, 4, 7, 12
12 1, 3, 4, 6, 7
——————————————————-

NBC executives are mainly concerned about the costs for the production. Consequently, they have set a goal of minimizing the number of cameras used. In seeking this objective, they want at least one camera to be available to cover each stadium area. Camera location 9 is the “blimp,” and it has been decided that the blimp must be used because of viewer expectation and fascination with the shots from this location. Stadium areas 1 and 2 are locker room locations. The viewer interest in football personalities has led the executives to request that at least two cameras be available to cover each of these areas.

(1) Formulate a ZOLP for the set covering problem that can be used to determine the minimum number of cameras that needed for coverage and where they should be set up.

(2) Run Solver to solve the ZOLP in (1) above. Be sure to copy and paste the Answer report at the appropriate place in your homework submission. What are the optimal solution and the optimal objective function value? What do they mean here?