Answer to Question #258070 in Operations Research for Dut Machar

Question

Consider the following problem

 

Maximize                   Z = 6_x1+8_x2

Subject to:

                                  5_x1+2_x2 ≤ 20

                                  X₁+2_x2≤ 10

And

                                 X_1≥ 0, X₂≥ 0

Answer 1

Solution:

1. To draw constraint 5x1+2x2≤20→(1)

Treat it as 5x1+2x2=20

When x1=0 then x2=?

⇒5(0)+2x2=20

⇒2x2=20

⇒x2=20/2=10

When x2=0 then x1=?

⇒5x1+2(0)=20

⇒5x1=20

⇒x1=20/5=4

2. To draw constraint x1+2x2≤10→(2)

Treat it as x1+2x2=10

When x1=0 then x2=?

⇒(0)+2x2=10

⇒2x2=10

⇒x2=10/2=5

When x2=0 then x1=?

⇒x1+2(0)=10

⇒x1=10

The value of the objective function at each of these extreme points is as follows:

The maximum value of the objective function Z=45 occurs at the extreme point (2.5,3.75).

Hence, the optimal solution to the given LP problem is : x1=2.5,x2=3.75 and max Z=45.