Answer to Question #185187 in Operations Research for Vaishali Tomar

Question

The optimal solution for the following LPP is Z* = 30 :

Max Z = X1 - X2 + 3X3

Subject to X1 + X2 + X3 less than or equal to 10

X1, X2, X3 greater than or equal to zero .

Answer 1

Given, Max $Z=x_1-x_2+3x_3$

subject to- $x_1+x_2+x_3\le 10~~~~~-(1)$

$x_1,x_2,x_3\ge 0$

Z=30( given)

$\Rightarrow x_1-x_2+2x_3=30~~~~~~~~~-(2)$

The solution to the above equation equation can be find by calculating optimal solution.

Solving eqn.(1) and (2) by taking $x_3$ as restricted variable , SO Taking $x_3$ =0

we get $x_1=20, x_2=-10,x_3=0$ .