Graph the feasibility region represented by the given inequalities and find the maximum profit if P = 4x + 5y. x ≥ 5 y ≤ 10 2x - y ≤ 8

First, graph the three inequalities: x ≥ 5, y ≤ 10, 2x - y ≤ 8

Next, look for the 3 intersections (vertices) of the lines: (5, 2), (5, 10), (9, 10)

Finally, input the vertex coordinates into P = 4x + 5y and look for the biggest #.

(5, 2) : 4 (5) + 5 (2) = 20 + 10 = 30

(5, 10) : 4 (5) + 5 (10) = 20 + 50 = 70

(9, 10) : 4 (9) + 5 (10) = 36 + 50 = 86

Answer: maximum profit = 86