Question #185187

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 .


1
Expert's answer
2021-05-11T18:26:16-0400

Given, Max Z=x1x2+3x3Z=x_1-x_2+3x_3


subject to- x1+x2+x310     (1)x_1+x_2+x_3\le 10~~~~~-(1)

x1,x2,x30x_1,x_2,x_3\ge 0


Z=30( given)

x1x2+2x3=30         (2)\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 x3x_3 as restricted variable , SO Taking x3x_3 =0


we get x1=20,x2=10,x3=0x_1=20, x_2=-10,x_3=0 .


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