Say in a linear programming problem a firm has an objective function it would like to maximize in the context of its constraints. The functions are Objective 40x + 30y C1 3x + 2y <= 54 C2 2x + 2y <= 40 C3 x +2y <= 35 and x, y >= 0.

a. What is the x, y pair for each of the points labeled A, B, D, and E, in the graph?

b. What is the value of the objective function at each point A, B, D, and E in the graph?

c. Which x, y pair has the highest value of the objective function and what is that value of the objective function at this pair?

d. If the objective function were to change to 40x + 32y, what would the value of the objective function be at A, B, D, and E points? Does the best x, y, pair change with this new objective function? What is the value of the objective function at the best point?

e. Going back to the objective of 40x + 30y, now say constraint C2 becomes 2x + 2y <= 44. Note C2 will shift out giving new points B' and D' (and you need to calculate the new values of these points). Of the points A, B', D', and E, which one is best and what is the objective function value at this point? How much did the objective function value increase with the RHS of C2 going up 4?