Total No. of Pages:
Register Number: 6995
Name of the Candidate:
P.G. DIPLOMA EXAMINATION, 2011
(APPLIED OPERATIONS RESEARCH)
(PAPER-II)
120. LINEAR, NON-LINEAR AND DYNAMIC PROGRAMMING MODELS
December] [Time : 3 Hours
Maximum : 100 Marks
Answer any FIVE questions(5×20=100)
- Use simplex method to solve the following LPP
Maximize Z=4x1+10x2
Subject to the constraints
2x1+x2 50,
2x1+5x2 100,
2x1+3x2 90,
x1, x2 0
- Solve by Dual simplex method the following LPP
Minimize Z=5x1+6x2
Subject to the constraints
x1+x2 2,
4x1+x2 4,
x1, x2 0
- The demand pattern for a product at consumer centers, A, B, C and D are 500 units, 7000 units, 4000 units and 2000 units, respectively. The supply for these centers is from three factories X, Y and Z. The capacities the factories are 3000 units, 6000 units and 9000 units respectively. The unit transportation cost in rupees from a factory to consumer center is given below in the matrix.
A / B / C / D
X / 8 / 9 / 12 / 8
Y / 3 / 4 / 3 / 2
Z / 5 / 3 / 7 / 4
Develop an optimal transportation schedule and find the optimal cost.
- Four different jobs are to be done on four machines, one job on each machine, as set up costs and time are too high to permit a job being worked on more than one machine. The matrix given below gives the time for producing jobs on different machines.
A / B / C / D
P / 10 / 14 / 22 / 12
Q / 16 / 10 / 18 / 12
R / 8 / 14 / 20 / 14
S / 20 / 8 / 16 / 6
Assign the jobs to machines so that total time of production is minimized.
-2-
- Solve the following NLPP using Kuhn Tucker conditions:
Maximize Z=x1+2x2–x23
Subject to the constraints
x1+x2 1,
x1, x2 0.
- Using quadratic programming solve the problem given:
Maximize Z=8x1–x12+4x2–x22
Subject to the constraints
x1+x2 2
x1, x2 0.
- Use dynamic programming to solve the following:
Maximize Z=x12+x22+x32
Subject to the constraints
x1+x2+ x3 10
x1, x2,x3 0.
- Write short notes on the following
i)Bellman’s optimality principles.
ii)Applications of dynamic programming
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