LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
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FIFTH SEMESTER – APRIL 2008
MT 5504 – OPERATIONS RESEARCH
Date : 06-05-08 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART-A
Answer all the questions (10 ´ 2 = 20)
1) What are the characteristics of operations research ?
2) Explain the terms slack and surplus variables.
3) What is meant by pure strategy ?
4) What is the value of the game ?
5) What is price break ?
6) What is an assignment problem?
7) Define traveling salesman problem.
8) What are the rules to be adopted in drawing the network ?
9) Write the difference between PERT and CPM ?
10) Define critical path.
PART- B
Answer any two questions (5 ´ 8 = 40)
11) A company produces two types of pens, say A and B. Pen A is a superior quality and pen B is lower quality. Profits on pen A and pen B are Rs.5 and Rs.3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. the supply of raw materials is sufficient only for 1000 pens of B per day. Pen A requires a special clip and only 400 clips are available per day. For pen B only 700 clips are available per day. Prepare a mathematical model so that the company can make maximum profit.
12) Solve by graphical method
Maximize Z = 5x + 8y
Subject to the constraints
2x + y £ 8
x + 3y £ 10 where x, y ³ 0
13) Solve the LPP by simplex method
Maximize Z = 20x + 30y
Subject to 3x + 2y £ 36
5x + 2y £ 50
2x + 6y £ 60 where x, y ³ 0.
14) Solve by dominance property the following game
player B
1 7 2
player A 6 2 7
6 1 6
15) Four jobs can be processed on four different machines, one job on one machine.
Resulting times in minutes vary with assignments are given bellow. Find the
optimum assignment of jobs to machines and the corresponding time.
Machines
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Jobs
16)
Determine the following: a path, a loop, a directed loop, a tree and a spanning
tree for the following network
17) Find the shortest route for the following network.
18) A manufacturer purchases 10,000 items per year for sales in his shop. The unit cost is Rs.10/year, the holding cost is 80 paise/month and cost of reordering is Rs.200. Determine economic lot size, optimal total yearly cost, number of orders per year and time between orders if shortages are not allowed.
PART- C
Answer any Two questions (2 ´ 20 = 40)
19) Solve the LPP by Big M- method, Minimize Z = 4x1 + x2
subject to 3x1 + x2 = 3
4x1 + 3x2 ³ 6
x1 + 2x2 £ 4 where x1, x2 ³ 0.
20) The following table gives the activities in a construction project.
Activity 1-2 1-3 2-3 2-4 3-4 4-5
Duration 20 25 10 12 6 10
Draw the network for the project. Find the critical path and project duration.
Find the total float for each activity.
21) (a) Solve the LPP by Dual Simplex method ,
Minimize Z = 3x + 2y
subject to 7x + 2y ³ 30
5x + 4y ³ 20
2x + 8y ³ 16 where x, y ³ 0
(b) Find the value of the following game by graphical method
( 10 + 10 )