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Posted By: kondapalli Member Level: Gold Posted Date: 08 May 2008
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2007 Jawaharlal Nehru Technological University B.Tech Electronics OPERATIONS RESEARCH setno1 Question paper
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1. (a) Discuss the different types of models used in OR.
(b) The ABC company combines factors X and Y to form a product which must
weigh 50kgs, At least 20kgs of X and no more than 40 kgs of Y can be used.
The cost of X is Rs.25 per kg. And that of Y is Rs.10 per kg. Use graphical
method to find the amounts of factors X and Y which should be used to
minimize total cost. [4+12]
2. Goods have to be transported from factories F1, F2 , F3 to warehouses W1,W2, W3
and W4 . The transportation costs per unit, capacities of the factories and require-
ments of the warehouses are given in the following table. Find the distribution with
minimum cost. [16]
To Capacities
10 7 5 3 15
From 9 12 10 2 10
12 6 8 5 30
Requirements 17 8 20 10
3. (a) What is a travelling salesman problem?
(b) Solve the following travelling salesman problem [4+12]
To
A B C D
A - 46 16 40
From B 41 - 50 40
C 82 32 - 60
D 40 40 36 -
4. (a) Equipment A costs Rs.9000. Annual operating costs are Rs.200 for the first
year and then increases by Rs.2,000 every year. Determine the best age at
which to replace the equipment.
(b) Equipment B costs Rs.10,000.Annual operating costs are Rs.400 for the first
year and then increases by Rs.800 every year. Now you have a equipment of
type A which is one year old. Should you replace it with B,if so when?
[8+8]
5. (a) For what value of a, the game with the following pay-off matrix is strictly
determinable?
Player A
Player B
B1 B2 B3
A1 A 6 2
A2 -1 A -7
A3 -2 4 a
(b) Differentiate between strictly determinable games and non strictly determinable
games. [12+4]
6. A stenographer has 5 persons for whom she performs stenographic work. Arrival
rate is poisson and service times are exponential. Average arrival rate is four per
hour with an average service time of 10 minutes. Cost of waiting is Rs 100 per hour
while the cost of servicing is Rs 50 each. Calculate:
(a) The average waiting time of an arrival
(b) The average length of the waiting line
(c) The average time which an arrival spends in the system, and
(d) The minimum cost service rate. [16]
7. (a) What is EOQ? Discuss step by step the development of EOQ formula.
(b) What are the advantages and disadvantages of increased inventory?
(c) Write a note on variables in inventory problem [8+4+4]
8. A man is engaged in buying and selling identical item. He operates from a ware-
house that can hold 500 items. Each month he can sell any quantity that he chooses
up to the stock at the beginning of the month. Each month he can buy as much as
he wishes for delivery at the end of the month. So long as his stock does not exceed
500 items. For the next four months he has the following error free forecasts of the
cost sales prices.
Month i 1 2 3 4
Cost Ci 27 24 26 28
Sales price Pi 28 25 25 27
If he currently has a stock of 200 units, what quantity should he sell and buy next
four months. Find the solution using dynamic programming. [16]
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