Optimization Theory BS Mathematics 8 Semester/Term BZU — Bahauddin Zakariya University 2022

9:36 AM

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85-664-18-22

BAHAUDDIN ZAKRIYA UNIVERSITY MULTAN

Final-Term Examination

Program: 85-4 Vears (Mathematics)

Course code: MATH 404

Time allowed: 2.5 Hours

Course Title: Optimization Theory

Semester 8i Session:(2018-2022)

Max Marks: 60

Sr.

No.

QI

Questions

(iti)

(Tv)

(%)

(vi)

(vill).

Q.2

Choose the correct answer.

An inequality constraint can be converted into equality by adding non-negative

variable named as:

la) slack variable:

(b) canonical variable

(c) artilicial variable

(e) none:

The maximum value of a function defined by / (x) - sin(x) is

(a) 1.57

(b) 3.14

Jc) 1

(d) o

Optimization means

(a) maximization

(b) minimization

(c) normalization Ya both a and b

Hessian matrix is a matrix consisting of all 2 order

derivative

(a) ordinary

(b) partial

(c) total

(d) mixed

Dual of dual is:

(a) dual

(b) primal

(c) optimal

(d) both b and c

Kuhn tucker conditions are used for multi dimensional

(a) equality constraints

(b) inequality constraints

(c) un constraints

(d) none

Method to solve multidimensional optimization problem with equality constraints are:

(a) direct substitution

(b) constrained variation

(e) Lagrange multipliers (2) all

The value of design variable represented by the corner points is known as:

(a) Optimal solution (bi feasible salution

(c) basic feasible solution

(d) none

Find dual of the following LPP.

тах z = 100+ 70у

Subjected to the constraints

5x + 10y ≤ 50

8x + 20y ≥ 18

3x - 2у = 6

Q.3

Q.4

Solve LPP using SIMPLEX method

Maximize:

Subjected to the constraints

2= 5x + 3y

3x + 5y ≤ 15

5x + 2y ≤ 13

x.Y≥0

Find initial basic feasible solution of following Transportation problem.

S.

32

19

70

40

D-

30

30

50

40

70

Demand

10

60

20

14

Supply

9

18

34

Q.5

Q.6

Minimize f(x)=x-y+2xº+2xysy" starting from point x=[0,0] upto 3 iterations by

Steepest Descent method

Determine maximum and minimum values of f(x)=4x5-25 x*+40 x'+10.

Q.7

Solve using graphical method

Maximize

2 = 2x + y

Subjected to,

5x + бу ≤ 32,

0.8

x.y ≥ 0

Maximize: 2 = 3x° + 4yº subjected to the constraints 2x - 3y =

10.

B5-664-18-22-200.

Max.

Marks

8

8

8

8

8