Solve the following linear programming problem graphically: Maximize subject to Z = 400x1 + 500x2 20x1 + 10x2 100 5x1 + 10x2 50 3x1x2 10 x1 + 4x2 15 x1, x2 0 a. Graph the constraints and identify the feasible region. (10 points) b. Draw the objective function, then determine the optimal solution(s) and the Maximum value of the objective function. (Show your calculation). (7 points) c. What other methods can you choose to find the optimal solution without drawing the objective function? Considering the structure of the feasible region, which method is better? Justify your answer. (3 points)