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Roll No. ......................
Total No. of Questions : 13]                                                         [Total No. of Pages : 03
Paper ID [A0515]
(Please fill this Paper ID in OMR Sheet)
MCA (305) (Old/S05) (Sem. - 3rd)
COMPUTER BASED OPTIMIZATION METHODS

Time : 03 Hours                                                             Maximum Marks : 75

Instruction to Candidates:
1) Section -A is Compulsory.
2) Attempt any Nine questions from Section - B.

Section - A<
(15 × 2 = 30)
Q1)
a) Write down various phases in solving an OR problem.
b) Illustrate graphically the unbounded problem of linear programming problem.
c) Solve the following problem graphically.
Maximize Z = 2x1 + x2 subject to x1 + 2x2 £ 10, x1 + x2 £ 6, x1 . x2 £ 2,
x1 . 2x2 £ 1, x1, x2 ³ 0.
d) Explain the role of surplus variables in the simplex method.
e) Write down the dual of the problem : maximize Z = 4x1 + 9x2 + 2x3,
subject to 2x1 + 3x2 + 2x3 £ 7, 3x1 . 2x2 + 4x3 = 5, x1, x2, x3 ³ 0.
f) Explain unbalanced transportation problem.
g) What is the transhipment problem?
h) How would you deal with the assignment problem where the object function is to be maximized?
i) Given below is an assignment problem, write it as a transportation problem:
A1 A2 A3
R1 1 2 3
R2 4 5 1
R3 2 1 4.
j) Explain Minimum matrix method for finding an initial basic feasible solution for a transportation problem.
k) The probability of shooting down an enemy aircraft by one rifle shot is 0.005. Find the probability of shooting down the plane with simultaneous shots from 250 rifles.
l) Explain clearly the term payoff table.
m) Write a short note on criterion of realism.
n) What are the disadvantages of revised simplex method over the original
simplex method.
o) Distinguish between pure and mixed integer programming problems.

Section - B
(9 × 5 = 45)
Q2) Discuss scientific methods in OR.
Q3) Using simplex method: Maximize Z = 5x1 + 3x2, subject to:
x1 + x2 £ 2, 5x1 + 2x2 £ 10, 3x1 + 8x2 £ 12, x1, x2 ³ 0.
Q4) Use the dual to solve the following L.P.P.:
Maximize Z = 3x1 . 2x2 subject to the constraints:
x1 £ 4, x2 £ 6, x1 + x2 £ 5, . x2 £ . 1; and x1, x2 ³ 0.
Q5) What is cycling? State the rules to avoid cycling.
Q6) A company has four plants P1, P2, P3, P4 from which it supplies to three markets M1, M2, M3. Determine the optimal transportation plan from the following data giving the plant to market shifting costs, quantities available at each plant and quantities required at each market. Market Plant Required at
Market
P1 P2 P3 P4
M1 19 14 23 11 11
M2 15 16 12 21 13
M3 30 25 16 39 19
Available 6 10 11 15 43 at plant
Q7) Solve the following transportation problem:
To
9 12 9 6 9 10 5
7 3 7 7 5 5 6
From 6 5 9 11 3 11 2
6 8 11 2 2 10 9
4 4 6 2 4 2 22
Q8) Explain the Hungarian method for solution of the assignment problems.
Q9) A salesman wants to visits cities A, B, C, D and E. He does not want to visit
and city twice before completing his tour of all the cities and wishes to return to the point of starting journey. Cost of going from one city to another (in rupees) is shown in the following table:
A B C D E
A 0 2 5 7 1
B 6 0 3 8 2
C 8 7 0 4 7
D 12 4 6 0 5
E 1 3 2 8 0
Find the least cost route.
Q10) Explain Decision-tree analysis. What is node in a decision tree?
Q11) Use revised simplex method to solve the L.P.P.: Maximize Z = x1 + x2
subject to the constraints: 3x1 + 2x2 £ 6, x1 + 4x2 £ 4, x1, x2 ³ 0.
Q12) Use branch and bound method to solve the following integer L.P.P.:
Maximize Z = 7x1 + 9x2 subject to the constraints: . x1 + 3x2 £ 6,
7x1 + x2 £ 35; x2 £ 7, x1, x2 ³ 0, and are integers.
Q13) Use dynamic programming to find the value of minimize Z = 2
3
2
2
2
y1 + y + y
subject to the constraints: y1 + y2 + y3 ³ 15, y1, y2, y3 ³ 0.


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