Identify the feasible region for the following set of constr

Identify the feasible region for the following set of constraints:

0.5A+0.25B>=30

1A+5B>=250

0.25A+0.5B<=50

A,B>=0

Solution

Start making a graph of the region. I\'d put A on the horizontal axis and B on the vertical. Conveniently, none of these is a strict inequality, so all the borders are included in the region.

A,B ? 0 confines the region to the first quadrant.
1A ? 150 gives us a vertical boundary at (150, 0).

2A - 1B ? 200
intersects that vertical boundary at (150,100) and slants from there down to the A-axis at (100,0). Points in the feasible region must be on or above this line, so that cuts off a small corner at the lower right of the region.

3A - 2B ? 0
runs from the origin to (150, 225). Points above it are excluded, so this confines the feasible region to a quadrilateral and its interior, with vertices at
(0,0), (150,225), (150,100), and (100,0).