Answer:
Step-by-step explanation:
We have to first find the vertices of the feasible region before we can determine the max value of P(x, y). We will graph all 4 of those inequalities in a coordinate plane and when we do that we find that the region of feasibility is bordered by the vertices (0, 0), (0, 1), (2, 3), and (5, 0). Filling each x and y value into our function will give us the max value of that function.
Obviously, when we sub in (0, 0). we get that P(x, y) = 0.
When we sub in (0, 1) we get 24(0) + 30(1) = 30.
When we sub in (2, 3) we get 24(2) + 30(3) = 138.
When we sub in (5, 0) we get 24(5) + 30(0) = 120.
Obviously, the vertex of (2, 3) maximized our function for a value of 138.
