OPERATIONS RESEARCH
Q1.
A) Explain the principles of Modeling in operation research.
B) PARLOR Ltd has two products Heaven and Hell. To produce one unit of Heaven, 2 units of material X and 4 units of material Yare required. To produce one unit of Hell, 3 units of material X and 2 units of material Y are required. Only 16 units of material X and 16 units of material V are available. Material X cost Rs. 2.50 per unit and Material Y cost Rs. 0.25 per unit respectively. Formulate an LP Model and solve it graphically. (1 0)
Q2. Carefree Corporation has four plants each of which can manufacture anyone of the four products. Product costs differ from one plant to another as follow:
|
Product
|
|
Plant
|
1
|
2
|
3
|
4
|
|
A
|
33
|
40
|
43
|
32
|
|
B
|
45
|
28
|
31
|
23
|
|
C
|
42
|
29
|
36
|
29
|
|
D
|
27
|
42
|
44
|
38
|
You are required to obtain which product each plant should produce to minimize cost
Q3. Find the basic feasible solution of the transportation problem by north-west 20 corner rule. Also find the optimal transportation plan.
|
|
1
|
2
|
3
|
4
|
5
|
Availability
|
|
A
|
4
|
3 |
1
|
2
|
6
|
80
|
|
B
|
5
|
2
|
3
|
4
|
5
|
60
|
|
C
|
:3
|
5
|
b
|
3
|
2
|
40
|
|
D
|
2
|
1
|
1
|
5
|
3
|
20
|
Q4 Determine the optimum strategies and value of the following game.
|
|
B
|
|
A
|
|
1 |
2
|
3
|
4
|
5
|
|
I
|
10
|
4
|
2
|
9
|
1
|
|
II
|
7
|
6
|
5
|
7
|
8
|
|
III
|
3
|
5
|
4
|
4
|
9
|
|
IV
|
6
|
7
|
3
|
3
|
2
|
Q5. A) Explain the various applications of Queuing Models
B) A Bank has only ore typist. Since the tyrIng work varies in length (number of pages to he typed), the typing rate is randomly distributed approximati-ig a poison distributiol with mean service rate of 8 letters per hour. The letters arrive at rate of 6 per hour during the entire B hours work day. If the type writer is valued at Rs. 1.50 per hour. determine
1. Equipment Utilization
2. The percentage time that an arriving letter has to wait
3. Average system time
4. Average cost due to waiting on the part of typewriter
Q6. Obtain the inverse of following matrix (10)
7 2 1
0 3 -1
-3 4 -2
B) A client asks an estate agent to sell three properties A, B and C for him and agrees to pay him 5% commission on each sale. He specifies certain conditions. The estate agent must sell property A first, and this he must do within 60 days. If and when A is sold the agent receives 5% commission on that sale. He can either back out at this stage or nominate and try to sell one of the remaining two properties with En 60 days. If he does not succeed in selling the nominated property in that period, he is not given the opportunity to sell the other. If he does sell it in the period, he is given the opportunity to sell the third property on the same conditions. The following table summarizes the prices, selling cost, (incurred by the estate agent whenever sale is made) and the estate agent's estimated probability of making sale. (10)
|
Property
|
Price of the
Property
|
Selling
cost
|
Property
of Sale
|
|
A
|
Rs. 12,000
|
Rs. 400
|
0.7
|
|
B
|
Rs. 25.000
|
Rs. 225
|
0.6
|
|
C
|
Rs. 50,000
|
Rs. 450
|
0.5
|
i. Draw up an appropriate decision tree for the same estate agent
ii. What is the estate agent's best strategy under EMV approach
Q7. Write short notes on the following
a) OR packages for simulation
b) Sensitivity Analysis