Bhavnagar University 2007 M.Sc Mathematics OPERATIONS RESEARCH - Question Paper

M.Sc. DEGREE EXAMINATION, DECEMBER 2007.
Mathematics
OPERATIONS RESEARCH
Time : 3 hours Maximum : 100 marks
ans any 5 ques..
1. (a) Solve the subsequent issue by Simplex method.
Maximize
Subject to

(b) Use dual Simplex method, solve the LPP :
Minimize
Subject to

2. (a) Use revised Simplex method to solve the LPP :
Maximize
Subject to

(b) Solve the subsequent integer issue :
Maximize
Subject to

3. A company has 5 salesmen, who have to be allocated to 4 marketing zones. The return from every zone depends upon the number of salesmen working in that zone. The expected returns for various number of salesmen in various zones, as estimated from the past records are provided beneath. Determine the optimal allocation policy.
Number of
Salesmen Marketing Zones
I II III
0 45 30 35
1 58 45 45
2 70 60 52
3 82 70 64
4 93 79 72
5 101 90 82
4. (a) A decision issue has been expressed in the subsequent pay-off table.
Letting to represent the sizes of composites and to the level of attendance.
S1 S2 S3 S4
a1
5 10 18 25
a¬2 8 7 12 23
a3 21 18 12 21
a4 30 22 19 15
Determine the optimal strategy under :
(i) Laplace criterion
(ii) Minimax criterion
(iii) Hurwitz criterion with .
(b) Use the dominance to simplify the rectangular game with the subsequent pay-off, and solve it graphically.
Player K
I II III IV
1 18
4 6 4
Player L 2 6 2 13 7
3 11 5 17 3
4 7 6 12 2
5. (a) What are the 3 time estimates in PERT?
(b) A project consists of the subsequent activities and time estimates.
Activity Least time
(in days) Greatest time
(in days) Most likely time
(in days)
1–2 3 15 6
1–3 2 14 5
1–4 6 30 12
2–5 2 8 5
2–6 5 17 11
3–6 3 15 6
4–7 3 27 9
5–7 1 7 4
6–7 2 8 5
(i) Draw the network.
(ii) What is the probability that the project will be completed in 27 days?
6. (a) Find the optimal order volume for a product for which the price-break is as follows :
Quantity Unit cost

Rs. 10

Rs. 9

Rs. 8
The monthly demand for the product is 200 units, the cost of the storage is 25% of the unit cost and ordering cost is Rs. 20.00 per order.
(b) A manufacturer has to supply his customer with 600 units of his products per year. Shortage are not allowed and storage cost amounts to 60 paise per unit per year. The set up cost is Rs. 80.00, obtain
(i) The economic order volume
(ii) The minimum avg. yearly cost
(iii) The optimum number of orders per year.
7. Show that for model, the probability distribution of queue length is , and
, obtain :
(a) The avg. number of customers in the system
(b) The avg. queue length.
8. (a) A T.V. repairman obtains that the time spent on his job has an exponential distribution with mean 30 minutes.
If he repairs sets in the order in which they came in and if the arrival of sets is Poisson with an avg. rate of 10 per eight hour day, what is his expected idle time day? How many jobs are ahead of the avg. set just brought in?
(b) A petrol station has 2 pumps. The service time follows the Exponential distribution with mean four minutes and cars arrive for service in a Poisson process at the rate of
10 cars per hour. obtain the probability that a customer has to wait for service. What proportion of time the pump remains idle?

Earning:   Approval pending.