Question

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

Objective Function
z = 21x - 25y

Constraints
0 ≤ x ≤ 5
0 ≤ y ≤ 8
4x + 5y ≤ 30
4x + 3y ≤ 20
A. Maximum: 105; at (5, 0)
B. Maximum: -150; at (0, 6)
C. Maximum: 0; at (0, 0)
D. Maximum: -98.75; at (1.25, 5)