Find the maximum andor minimum values of the objective funct

Find the maximum and/or minimum value(s) of the objective function on the feasible set S. (If an answer does not exist, enter DNE.) Z = 5x + 8y maximum minimum

Solution

Let us substitute points (0,7), (1,5), (4,2), (8,0) and (8,7) in the function Z = 5x +8y

(0,7) ; Z = 5(0) + 8(7) = 56

(1,5) ; Z = 5 + 40 = 45

(4,2) ; Z = 20 + 16 = 36

(8,0) : Z = 40 + 0 = 40

(8,7) : Z = 40 + 56 = 96

Maximum value of the objective function on the feasible set is 96 at (8,7)

Minimum value of the objective function on the feasible set is 36 at (4,2)