LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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B.Sc. DEGREE EXAMINATION –MATHEMATICS
FIFTH SEMESTER – APRIL 2007
MT 5504 – OPERATIONS RESEARCH
Date & Time: 03/05/2007 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
SECTION –A
Answer All: 2 x 10 = 20
- Define Operations Research.
- What are the three methods to find Initial Basic Feasible solution in Transportation problem ?
- Solve the Transportation problem by Least Cost Method.
| A1 | A2 | A3 | Supply | |
| B1 | 4 | 6 | 2 | 5 |
| B2 | 3 | 1 | 5 | 15 |
| B3 | 4 | 5 | 3 | 15 |
| Demand | 10 | 10 | 10 |
- Solve the game:
| 2 | 1 | 4 |
| 1 | 4 | 3 |
| 2 | 2 | 6 |
- Define Unbalanced situation in Transportation problem.
- Define Feasible Solution.
- Solve the Assignment problem
| 3 | 7 | 5 |
| 4 | 7 | 2 |
| 5 | 4 | 6 |
- What is Dummy activity in Network problem ?
- Define Optimistic Time Estimate.
- Define Economic Order Quantity.
SECTION –B
Answer any five: 5x 8 = 40
- Find the Initial Basic Feasible solution in Transportation problem using i) North West Corner Rule ii) Least Cost Method.
| A1 | A2 | A3 | A4 | Supply | |
| B1 | 4 | 2 | 1 | 3 | 20 |
| B2 | 8 | 4 | 2 | 4 | 20 |
| B3 | 1 | 2 | 3 | 4 | 30 |
| B4 | 5 | 2 | 4 | 6 | 20 |
| Demand | 10 | 30 | 10 | 40 |
- Using Graphical method solve the Linear Programming Problem
Max z = 2x1+4x2 subject to the constraints
2x1+4x2 ≤ 5 , 2x1+4x2 ≤ 4, x1, x2 ≥ 0.
- Solve the Assignment problem
| M1 | M2 | M3 | M4 | M5 | |
| J1 | 9 | 22 | 58 | 11 | 19 |
| J2 | 43 | 78 | 72 | 50 | 63 |
| J3 | 41 | 28 | 91 | 37 | 45 |
| J4 | 74 | 42 | 27 | 49 | 39 |
| J5 | 36 | 11 | 57 | 22 | 25 |
- Solve using Matrix Oddment method
| -1 | 2 | 1 |
| 1 | -2 | 2 |
| 3 | 4 | -3 |
- Define critical path and draw the Network diagram for
Activity: A B C D E F G H I J K
Immediate predecessor: – – – A B B C D E H,I F,G
- Solve using Dominance property
| 1 | 7 | 3 | 4 |
| 5 | 6 | 4 | 5 |
| 7 | 2 | 0 | 3 |
- Solve the Transportation problem
| A1 | A2 | A3 | A4 | Supply | |
| B1 | 1 | 2 | 1 | 4 | 30 |
| B2 | 3 | 3 | 2 | 1 | 50 |
| B3 | 4 | 2 | 5 | 9 | 20 |
| Demand | 20 | 40 | 30 | 10 |
- The probability distribution of monthly sales of certain item is as follows:
Number of items: 0 1 2 3 4 5 6
P(d) : 0.02 0.05 0.30 0.27 0.20 0.10 0.06
The cost of carrying inventory is Rs 10 per unit per month . Find the
shortage cost for one item for one unit of time.
(P.T.O)
SECTION –C
Answer any two: 2x 20 = 40
- Solve the following Linear Programming Problem using Simplex method
Max z = 3x1+2x2 subject to the constraints
x1+2x2 ≤ 6 , 2x1+x2 ≤ 8, -x1+x2 ≤ 1, x2 ≤ 2, x1, x2 ≥ 0. (20)
20 a) Solve the Transportation problem to maximize the profit
| A1 | A2 | A3 | A4 | Supply | |
| B1 | 40 | 25 | 22 | 33 | 100 |
| B2 | 44 | 35 | 30 | 30 | 30 |
| B3 | 38 | 38 | 38 | 30 | 70 |
| Demand | 40 | 20 | 60 | 30 |
- b) Solve the following traveling sales man problem
| A | B | C | D | E | |
| A | – | 3 | 6 | 2 | 3 |
| B | 3 | – | 5 | 2 | 3 |
| C | 6 | 5 | – | 6 | 4 |
| D | 2 | 2 | 6 | – | 6 |
| E | 3 | 3 | 4 | 6 | – |
(10+10)
21 a) Solve the game graphically
| 1 | 0 | 4 | -1 |
| -1 | 1 | 2 | 5 |
- b) The annual demand for an item is 3200 units, the unit cost is Rs 6 and inventory
Carrying charges 25% per annum. If the cost of one procurement is Rs 150. Find
- i) Economic Order Quantity ii) Time between two consecutive orders
iii) Number of orders per year iv) The optimal total cost (10+10)
22 a) Draw the Network diagram ,the Critical path ,the project duration and the total float
for the following activities
Activity: 1-2 2-3 3-4 3-7 4-5 4-7 5-6 6-7
Duration: 3 4 4 4 2 2 3 2
- b) What is the probability that the project will be completed in 27 days? Draw the
network diagram also .
Activity: 1-2 1-3 1-4 2-5 2-6 3-6 4-7 5-7 6-7
T0 : 3 2 6 2 5 3 3 1 2
Tm : 6 5 12 5 11 6 9 4 5
Tp : 15 14 30 8 17 15 27 7 8
(10+10)
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