Resolve MAX Z 25x1 75x2 ST 15x1 40x2 270 12x1 50x2 270 1

Resolve:

MAX Z = 25x1 + 75x2

ST

15x1 + 40x2 270

12x1 + 50x2 270

1. Given that x1 and x2 are in the basis, i.e., non zero in the solution to this LP, compute the elements of the final tableau using the relevant matrix equations.

2. Compute the permissible range over which the cost coefficient of variable x1 may be varied without changing the basis.

Solution

Subject to the constraints , x & Y, maximize 25 X1+75X2

First equation

15X1+40X2=270

If x1=0, then X2 =6.75

If X2= 0, X1 = 18

Second Equation

12X1+50X2=270

X1= 0, y = 5.4

X2= 0 . X1 = 22.5

Now, 60X1+160X2= 1080 ( Multiplied the equation by 4)

          60X1+250X2= 1350( Multiplied the equation by 5)

-90X2= -270

X3 =3

X1 = 10

The profit maximization is 25x1+75X2

Units                          Profit

0,6.75                      506.25

18,0                         450

0,5.4                         405

22.5,0                          562.5

10,3                            475

The profit will be maximized at X= 22.5 units & X2 = 0 Units