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
