## 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.