Question: Find the maximum and the minimum, if they exist, of

z = 6x + 2y

subject to the constraints

x + y ≥ 16

4x + 2y ≥ 48

x ≥ 0, y ≥ 0

If the optimum value does not exist, explain why. The graph of the feasible region must be included in the solution to earn full credit.