Problem 3 15 Identify the feasible region for the following

Problem 3 (15)
Identify the feasible region for the following set of constraints:

3x1-2x2 0

2x1-1x2 200

1x1 150

x1,x2 0

Im getting confused by the second constraint, i keep getting a negative x2.

Solution

Identify the feasible region for the following set of constraints:

3x1-2x2 0

2x1-1x2 200

1x1 150

x1,x2 0

3x1 - 2x2 0 is equivalent to -2x2 -3x1, or x2 (3/2)x1.

by the graphical representation this would be the side of the linex2 = (3/2)x1 that includes the point (1, 0), i.e. below and to the right.

2x1- x2 200 is equivalent to -x2 200 - 2x1, or x2 2x1 - 200. This is the side above the line x2 = 2x1 - 200.

x1 150 is the region to the left of the line x 1= 150.

substitue x1=0 which implies x2=0

x1=150 which implies x2=225,100

x1=100 then x2=0

The feasible region consists of a quadrilateral with vertices (0, 0), (150, 225), (150, 100), and (100, 0).