Find the value of the objective function z = 6x

Question

Find the value of the objective function z = 6x - 5y at each of the vertices (0, 6), (2, 6), (-2, -2), and (5, -2) and then state the maximum and minimum values of the function.
A) maximum 40, minimum -30
B) maximum -30, minimum 40
C) maximum 40, minimum 30
D) maximum 30, minimum -30

Quizplus · Accepted Answer

For each vertex, we calculate the value of the objective function z = 6x - 5y:- At (0, 6), z = 6(0) - 5(6) = -30- At (2, 6), z = 6(2) - 5(6) = 12 - 30 = -18- At (-2, -2), z = 6(-2) - 5(-2) = -12 + 10 = -2- At (5, -2), z = 6(5) - 5(-2) = 30 + 10 = 40The maximum value of the function is 40, and the minimum value is -30.