Question

Find the values of x and y that maximize the objective function P=3x+2y for the graph. What is the maximum value?

Answer 1

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

NOTE: I don't understand why (5,4) was given on your graph as a vertex.

(0,8): P = 3(0) + 2(8)  = 0 + 16   = 16

(5,4): P = 3(5) + 2(4)  = 15 + 8   = 23

(9,0): P = 3(9) + 2(0)  = 27 + 0   = 27      THIS IS THE LARGEST (MAX) P-VALUE

Answer: 27