What is the maximum value of P = 24x + 30y, given the constraints on x and y listed below? x+y (less than or equal to) 5 x-y (greater than or equal to) - 1 x (greater than or equal to) 0 y (greater than or equal to) 0 120 132 138 150

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.