Question

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

If you rewrite the constraints in terms of y, for example,
2x+y≤30 as
y≤-2x + 30
then you can graph the constraints.
When y≤ something, then the feasible region is below the line, if y>0, the feasible region is above the line.
For x≥0, it is on the right of the y-axis.

What do you get for the corner points?

Once you have the corner points in the form of (x,y), you can evaluate
Z(x,y) in terms of x and y and hence compare the value of Z that maximizes its value.