Answer to Question #241996 in Operations Research for Lateef

Question

Solve the following problem Linear programming problem.
Marimize :
Z= x+ 2x + x
Subject to :
2x+3x +3x ≤11
x↑j € Zj= 1, 2, 3, 4

Answer 1

Solution:

Assume the given broblem is

Max Z=x1+2x2+x3 subject to

2x1+3x2+3x3≤11 and 

x1,x2,x3≥0;

The problem is converted to canonical form by adding slack, surplus and artificial variables as appropriate

(1) As the constraint-1 is of type '≤' we should add slack variable S1

After introducing slack variables

Max Z=x1+2x2+x3+0S1 subject to

2x1+3x2+3x3+S1=11 and 

x1,x2,x3,S1≥0

Since all Zj-Cj≥0

Hence, optimal solution is arrived with value of variables as :

x1=0,x2=3.6667,x3=0

Max Z=7.3333