Find the value of the objective function z = 8x

Question

Find the value of the objective function z = 8x - 4y at each of the vertices (-4, 9), (-2, -7), (-2, -5) (4, 8), and then state the maximum and minimum values of the function.
A) maximum -68, minimum 68
B) maximum 12, minimum 68
C) maximum -68, minimum 12
D) maximum 12, minimum -68

Quizplus · Accepted Answer

The value of the objective function z = 8x - 4y at each vertex is calculated as follows:- At (-4, 9), z = 8(-4) - 4(9) = -32 - 36 = -68.- At (-2, -7), z = 8(-2) - 4(-7) = -16 + 28 = 12.- At (-2, -5), z = 8(-2) - 4(-5) = -16 + 20 = 4.- At (4, 8), z = 8(4) - 4(8) = 32 - 32 = 0.Therefore, the maximum value of the function is 12, and the minimum value is -68.