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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 setno4 Question paper
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1. (a) Construct the dual of the problem.
Minimize Z = 3X1 - 2X2 + 4X3
Subject to the constraints
3X1 + 5X2 + 4X3 7
6X1 + X2 + 3X3 4
7X1 - 2X2 - X3 10
X1 - 2X2 + 5X3 3
4X1 + 7X2 - 2X3 2 and
X1, X2, X3 0
(b) Solve the following LPP by using Simplex method.
Maximize Z = 45X1 + 80X2
Subject to
5X2 + 20X2 400
10X1 + 15X2 450 and
X1, X20 [4+12]
2. A Company has four factories from which it ships its product units to four ware-
houses which are the distribution centres. Transportation costs per unit between
various combinations of factories and warehouses are as : [16]
Factory Warehouse Available
1 2 3 4
1 48 60 56 58 140
2 45 55 53 60 260
3 50 65 60 62 360
4 52 64 55 61 220
Requireed 200 320 250 210
Find the transportation schedule which minimizes the distribution cost.
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. There are two offers of coal handling equipment in a thermal power station
Offer A; cost; Rs.20,00,000 capacity:200 tons/hr
Block I II III IV V VI
Operating-com-maintenance 120 130 140 160 190 220
cost per year(in Rs thousand)
Resale(salvage value in Rs Thousand) 1600 1550 1450 1300 1100 800
Offer B; cost:Rs.40,00,000 capacity:300 tons/hr
Block I II III IV V VI
Operating-com-maintenance 140 145 151 160 172 190
cost per year (in Rs thousand)
Pesale (salvage value) in Rs thousand 3500 3400 3250 3050 2800 2500
Each block is of 5 years duration
Which offer should be accepted consistent with optimum replacement policy for
minimum average annual cost? [16]
5. (a) Consider the following pay-off matrix and determine the optimal strategy.
B
A
I II III
I 6 9 4
II 5 10 7
III 9 8 9
(b) Write a note on zero-sum games [12+4]
6. Mumbai post-office has 3 speed-post window-counters. It receives on average 45
customers per hour. Arrivals are poisson distributed and service time exponentially
distributed. The post office serve on average 15 customers per hour.
(a) What is the probability that a customer will be served immediately?
(b) What is the probability that a customer will have to wait?
(c) What is the average total time that customer must spend in the post-office.
[16]
7. A baking company sells cake by kg weight. It makes a profit of Rs.5 per kg on each
kg sold on the day it is baked. It disposes of all cakes not sold on the day it is
baked at a loss of Rs.1.20 a kg. If the demand is known to be rectangular between
2000 and 3000 kgs. Determine the optimal daily amount baked. [16]
8. Solve the following model of the optimal subdividing of a cable of length 10 units
into three parts such that the product of their lengths is maximized, using dynamic
programming technique.
Maximize Z = p1Xp2Xp3
Subjected to p1 + p2 + p3 = 10; p1, p2and p3 0 [16]
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