Problem 1 (25 points) Solve the following linear programming problem graphically: Minimize Z = 4x1 + 3.6x2

subject to

3x1 + 4x2 36

11x1 + 5x2 55

4x1 9x2 0

x1, x2 0

a. Graph the constraints (make sure to label them clearly to indicate which line corresponds to which constraint) and identify the feasible region (Shade/darken the feasible region). Provide all necessary steps/calculations to justify your answers. (10 points)

b. Using the corner point method, determine the optimal solution(s) and the minimum value of the objective function. Provide all necessary steps/calculations to justify your answers. (8 points)

c. Are any constraints redundant? Justify. (2 points)

d. If the objective function is Maximize Z = 4x1 + 3.6x2, what would the optimal solution(s) and the value of the objective function be? Justify your answer. (2 points)

e. For the optimal solution of part d (i.e., the maximization of Z), determine the slack/surplus that would result for each constraint. (3 points)

PLEASE ONLY ANSWER PARTS C, D, E PLZ!! Thank you!!