## OPTIMIZATION TECHNIQUES JNTU previous years question papers

Time: 3 hours Max Marks: 80

Answer any FIVE Questions.

All Questions carries equal marks.

1. Solve using Kuhn-Tucker Conditions
Maximize z = 2x1 – x1
2 + x2 subject to the constraints
2x1+3x2 = 6
2x1+x2 = 4
x1, x2 = 0[16]

2. Using method of Langrangian multipliers solve
Minimize Z = x12+ x22+ x32
subject to
4x1 + x22 + 2x3 = 14; x1, x2, x3 = 0[16]

3. Using Simplex method solve the linear programming problem
Maximize Z = 4x1+ 3x2 + 4x3 + 6x4
Subject to x1+ 2x2 + 2x3 + 4x4 = 80
2x1+ 2x3 + x4 = 60
3x1+ 3x2 + x3 + x4 = 80
x1, x2, x3, x4 = 0
[16]

4. Solve the following transportation problem by vogel’s approximation method and check the optimality of the solution. The unit cost of shipment are given in the cells below
To From D E F G Supply
A 11 13 17 14 250
B 16 18 14 10 300
C 21 24 13 10 400
Demand 200 225 275 250
[16]

5. Minimize f[x]= 0.65-[0.75/[1+x2]] – 0.65 tan-1[1/x] in the interval [0,3] by the Fibonacci method using n=6

6. Using Powel’s method
Minimize x1-x2 + 2x1
2 +2x1x2 +x2
2 from the starting point x1= [0,0]
[16]

7. Using Steepest descent method
Minimize x12 – x1x2 + 3x2
2. Take starting point [1,2]
[16]

8. What are the essential characteristics of dynamic programming problems? Describe dynamic programming as an approach for solving multistage decision process.

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