Question

1. Maximize z = 16x + 8y subject to:
2x + y ≤ 30
x + 2y ≤ 24
x ≥ 0
y ≥ 0
Graph the feasibility region.
Identify all applicable corner points of the feasibility region.
Find the point(s) (x,y) that maximizes the objective function z = 16x + 8y.

Answer 1

The corner points are, by inspection:
<i>(0,30)</i>,(0,12), (15,0), <i>(24,0)</i>,
and (12, 6)[inters. of the two lines].
The points in italics do not satisfy at least one constraint.
Now evaluate the objective function at each of the feasible corner points and select the one that maximizes the objective function.
If there are two points that give the same maximum value of the objective function, then any point that lie on the line joining the two points and is located between the two points maximizes the objective function.