Question

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

Answer 1

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