Question

Solve the following Linear Programming (LP) problem:

Maximize Z = 3X1 + 2X2

Subject to: X1 + X2 ≤ 6

2X1 + X2 ≤ 8

-X1 + X2 ≤ 1

X2 ≤ 2

a) Identify the feasible extreme points (maximum attractive corner) for the problem.

b) Solve the problem graphically.

Answer 1

The function increases as $x_1$ and $x_2$ increase. The problem is considered in the following polygon:

We draw lines of the type $z=3x_1+2x_2$, where we set $z=c_1,c_2,...$ with arbitrary $c_j$. We receive the picture:

It is clear that the maximum is achieved at the point C. It is situated at the intersection of lines $x_2=2$ and $2x_1+x_2=8$ . We get $C=(3,2)$. The maximum is: $Z=13$