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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 & computers OPERATIONS RESEARCH setno3 Question paper
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1. Using the principle of duality solve the following LPP.
Minimize Z=2X1+2X2
Subject to
2X1+4X21
X1+2X21
2X1+X21 and X1,X20 [16]
2. A Securable Sales Group wishes to purchase the following quantities of uniforms:
Uniform type : A B C D E
Quantity: 150 100 75 250 200
Tenders are submitted by four different manufacturers who undertake to supply
not more than the quantities indicated below.
Manufacturers: P Q R S
Total uniform quantity: 300 250 150 200
The group estimates that its profit (in Rs. ) per uniform will vary with the
manufacturer as shown in the following table :
A B C D E
P 27.50 35.00 42.50 22.50 15.00
Q 30.00 32.50 45.00 17.50 10.00
R 25.00 35.00 47.50 20.00 12.50
S 32.50 27.50 40.00 250.00 17.50
How should the orders for uniforms be placed. [16]
3. (a) Give three different practical application of sequencing algorithm
(b) Suppose several types of furniture must pass through three pre finishing stages
in the same order. Because of the size and complexity of each type of furniture
the processing time at each stage varies considerably
Stage Stage1 Stage2 Stage3
Type
Chair 7 2 5
Desk 10 3 8
Lamp 6 4 4
Table 7 3 2
Coffee Table 8 5 2
i. Determine an optimal sequence.
ii. What is the total elapsed time for an optimal sequence.?
iii. What is the total idle time at stages 1, 2 and 3 ? [6+10]
4. (a) Running cost and resale value of a small machine whose purchase price is
Rs.6000 are given below
Year 1 2 3 4 5 6 7
Running cost(Rs.) 1000 1200 1400 1800 2300 2800 3400
Resale value(Rs.) 3000 1500 750 375 200 200 200
Determine at what age replacement is due?
(b) Let the owner has three of above type machines, two of which are two years
old. Now he is considering a new type of equipment with 50% more capacity
than one of the old ones at a unit price of Rs.8000 with the running costs and
resale price as follows:
Year 1 2 3 4 5 6 7 8
Running cost (Rs.) 1200 1500 1800 2000 3100 4000 5000 6100
Resale price (Rs.) 4000 2000 1000 500 300 300 300 300
Assuming the loss of flexibility due to fewer machines is of no importance
and that he will continue to have sufficient work for three of the old machine,
what should his policy be? [6+10]
5. Solve the following game by algebraic method [16]
A
B
1 2
1 -2 -4
2 -1 3
3 1 2
6. Assume in a hotel a server is to look after supply of three tables, which would
accommodate in total six customers. Assume customers who arrive when all the
six seats of the three tables are full. Customers arrive at the average rate of 4 per
hour and spend an average of 15 minutes in the hotel. Find
(a) The probability a customer can directly sit in a seat upon his arrival
(b) Expected number of customers waiting for a seat?
(c) The time a customer can expect to spend in the hotel?
[16]
7. (a) The Paintwell paint ltd. would like to improve its inventory facilities for its
supply of paints used for automobiles. Annual demand for the paint is 50,000
litres and the paint costs Rs.20 per litre and is used at a constant rate. Annual
carrying cost is 15% of the value of the paint held. Each order costs Rs.80.
Determine:
i. How much paint should be ordered each time?
ii. How often should paint be ordered
iii. Time between two consecutive orders.
(b) Mention the characteristics of inventory system. [12+4]
8. A distance network consists of 11 nodes which are distributed as shown in the fol-
lowing tables. Find the shortest path from node 1 to node 11 and the corresponding
distance. [16]
Arc Distance Arc Distance
1-2 8 5-8 12
1-3 7 5-9 7
1-4 1 6-9 9
2-5 5 7-9 6
3-5 9 7-10 13
3-6 2 8-11 4
3-7 8 9-11 2
4-7 10 10-11 15
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