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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 setno2 Question paper
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1. (a) Show on a graph the following:
i. Multiple optimum solution
ii. Redundant constraint.
(b) Solve the following LPP graphically:
Maximize Z = 0.75 x1 + x2
Subject to:
x1 + x2 5
x1 - x2 0
-0.5x1 + x2 1
x1 + 1.5 x2 3
x1, x2 0 [4+12]
2. X transport Company has four warehouses A,B,C and D. It is required to deliver
a product from these warehouses to three customers P,Q and R. The warehouses
have the following amounts in stock :
Warehouse : A B C D
Number of Units : 15 16 12 13
And the customers requirements are :
Customer : P Q R
Number of Units : 18 20 18
The table below shows the costs (in hundreds of rupees) of transporting one unit
from warehouse to the customer. Solve the problem to minimize the transportation
cost. [16]
A B C D
P 8 9 6 3
Q 6 11 5 10
R 3 8 7 9
3. (a) The owner of a small machine shop has four machinists available to assign to
jobs for the day. Five jobs are offered with the expected profit (in hundreds
of rupees) for each machinist on each job being as follows :
Machinist A B C D E
1 6 8 5 10 8
2 7 9 6 7 6
3 9 9 11 7 8
4 5 6 9 8 8
Find the assignment of machinists to jobs that result in a maximum profit.
Which job should be declined.
(b) Find the sequence that minimizes total elapsed time required to complete the
following jobs: [8+8]
Job nummber 1 2 3 4
Machine A 4 3 7 5
Machine B 6 7 8 4
4. (a) Briefly explain the reasons for replacement.
(b) The following table gives the running costs /year and resale price of equipment
whose purchase price is Rs.8000.
Year 1 2 3 4 5 6 7 8
Running Cost(Rs.) 2500 2600 2800 3100 3500 3900 4400 5400
Resale Value(Rs.) 6500 5500 4700 4200 3800 3500 3500 3500
i. At what year is replacement due?
ii. If the resale value is zero, will there be any change in the replacement
policy? [4+12]
5. (a) Briefly explain the general rules for dominance.
(b) Use dominance property to reduce the game to 2x2 game and hence find the
optimal strategies [4+12]
Player A
Player B
5 -10 9 0
6 7 8 1
8 7 15 1
3 4 -1 4
6. ABC Company has two desk top operators. Letter is dictated by the manager
and suppose that the letters to be typed arrive at random (following poisson dis-
tribution) at a rate of three per hour for each desk top operator. Suppose that
each operator can type five letters per hour on the average (following exponential
distribution):
(a) Assuming that each operator does her own work, what is the expected waiting
time for a letter?
(b) Suppose that the two operators are pooled. That is, letters are sent to the
two together and are done by whoever is free, in the order of arrival. What is
the expected waiting time for a letter under this arrangement? [16]
7. (a) What is inventory? Explain its importance in an industrial undertaking.
(b) What are the different types of inventories in industries.
(c) Describe various functions of inventory control. [8+3+5]
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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