Operational Research
1) Find the optimum strategies and the value of the game from the following pay off matrix concerning two person game.
|
Player B |
|
|
|
|
| Player A |
b1 |
b2 |
b3 |
b4 |
b5 |
| a1 |
6 |
3 |
-1 |
0 |
-3 |
| a2 |
3 |
2 |
-4 |
2 |
-1 |
2) An electric firm manufactures three types of computers, a standard model, portable model and a lap top. The production of a standard computer requires a capital of Shs. 250 and 30 hours of labour. The production of portable computers requires a capital expenditure of Shs. 250 and 30 hours of labour. The production of lap top requires a capital expenditure of Shs. 300 and 25 hours of labour. The firm has a Shs 20.000 capital and 2160 hours available for production of standard computers, portable computers and laptop. The firm incurs a cost of Shs. 320 on each standard computer, Shs. 220 on each portable computer and Shs. 280 on each lap top.
Required:
a) Formulate the mathematical model for this problem.
b) Obtain a dual program from primal program.
c) Determine the optimal product mix from formulated dual program so as to maximize on the expected return.
d) Deduce the optimal solution for the primal program.
OPERATIONAL RESEARCH
Instructions: Attempt all the questions
1) In a large maintenance department, fitters draw parts from the store which is at present staffed by one store nun. The maintenance foreman is concerned about the tune spent by fitters getting parts and has recommended the employments of a stare's laborer to assist the store man. On investigation, it was found that:
- A simple queue exists
- Fitters cast Sh. 250per hour
- The store man costs Sh. 200 per hour and can deal on average with 10 fitters [per hour].
- A laborer could be employed at 175, per hour and the capacity of the stores would be per hour in terms of service.
- On average 8 fitters visit the store each hour.
Required:
a) What percentage of the time is the store man idle before a laborer is employed?
b) How much time does a fitter spend in the store after the laborer is employed?
c) Determine whether it is worth while employing the laborer.
2) A firm produces four products. There are four operators who are capable of producing any of these four products. The firm records 8 hours a day and allows 30 minutes for lunch. The processing time in minutes and the profit for each of the products are given below.
|
Products |
|
|
|
| Operators |
A |
B |
C |
D |
| 1 |
15 |
9 |
10 |
6 |
| 2 |
10 |
6 |
9 |
6 |
| 3 |
25 |
15 |
15 |
9 |
| 4 |
15 |
9 |
10 |
10 |
| Profit(Sh.)Per Unit |
8 |
6 |
5 |
4 |
Required:
Determine the optimal assignment of operator to product so as to maximize the profit of the firm.
3) Queues are nuisance and should be eliminated. Discuss