Question

10. The optimal solution of a maximization type LPP is given in the following table:

C sj

′ 6 4 0 0 0 

Solution

CB 

Basic Variables 

1

x 2

x 3

x 4

x 5

x

0 3

x 0 5/3 1 − 3/2 0 14 

0 5

x 0 − 3/1 0 1/3 1 5 

6 1

x 1 2/3 0 1/3 0 8 

Cj − Z j

0 0 0 − 2 0 Z = 48

 (i) Find the alternative optimal basic feasible solution. 

 (ii) Find an alternative optimal non-basic feasible solution.

Answer 1

(i) $2x_1 + x_2 ≤1000\\ x_1 + x_2 ≤ 800\\x_1,x_2\ge0$

$Z=4x_1+3x_2$

The graphical region of the given inequalities is-

The critical points are-

(200,600)  $Z=4x_1+3x_2=4(200)+3(600)=800+1800=2600$

(500,0) $Z=4x_1+3x_2=4(500)+3(0)=2000+0=2000$

(0,800) $Z=4x_1+3x_2=4(200)+3(600)=0+2400=2400$

(0,0) $Z=4x_1+3x_2=4(0)+3(0)=0+0=0$

The maximum value of Z is 2600 at $x_1=200,x_2=600$

(ii) As calculating above,

The alternative non feasible solution is $x_1=500,y_1=0$