Loyola College B.Sc. Mathematics April 2007 Operations Research Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 

CV 16

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

 

  1. Define Operations Research.
  2. What are the three methods to find Initial Basic Feasible solution in Transportation problem ?
  3. 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

 

 

 

 

 

 

 

 

  1. Solve the game:
2 1 4
1 4 3
2 2 6

 

 

 

 

  1. Define Unbalanced situation in Transportation problem.
  2. Define Feasible Solution.
  3. Solve the Assignment problem
3 7 5
4 7 2
 5 4 6

 

 

 

 

  1. What is Dummy activity in Network problem ?
  2. Define Optimistic Time Estimate.
  3. Define Economic Order Quantity.

 

SECTION –B

Answer any five:                                                                              5x 8 = 40

 

  1. 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

 

 

 

 

  1. Using Graphical method solve the Linear Programming Problem

Max z = 2x1+4x2    subject to the constraints

2x1+4x≤ 5 ,       2x1+4x2 ≤ 4,         x1, x2 ≥ 0.

 

 

  1. 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

 

 

  1. Solve using Matrix Oddment method

 

-1  2  1
 1 -2  2
 3  4 -3

 

 

  1. 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

 

 

  1. Solve using Dominance property
1 7 3 4
5 6 4 5
7 2 0 3

 

 

 

 

 

  1. 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

 

 

 

 

 

 

 

 

  1. 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

 

  1. Solve the following Linear Programming Problem using Simplex method

Max z = 3x1+2x2    subject to the constraints

x1+2x≤ 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

 

 

 

 

 

 

 

  1. 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

 

 

 

  1. 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

  1. 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

 

  1. 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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