Suppose a manager wishes to find the optimal level of two activities X and Y, which yield the total benefits presented in the table below. The price of X is $40 per unit, and the price of Y is $100 per unit.

Level of Total Benefit of Total Benefit of Activity Activity X (TBx) Activity Y (TBy) O 0 0 800 1,000 2 1.440 1,900 H 3 2,000 2,700 4 2,360 3,400 5 2,680 4,000 6 2,960 4,500 7 3,200 4,900 8 3,400 5,200a The manager faces a budget constraint of $500 for expenditures on activities X and Y. The optimal levels of activities of X and Y when the manager can spend only $500 are X = and Y = b. In part a, the total benefit associated with the optimal level of X and Y is C. Now let the budget constraint increase to $780. The optimal levels of activities of X and Y when the manager can spend $780 are X = and Y= d. In part c, the total benefit associated with the optimal level of X and Y is S