Suppose that you can schedule a worker for up to 4 hours per day.The total benefit and total cost functions are B(H)= 1,300H - 20H² and C(H)= 500H + 60H².The corresponding formulas for marginal benefit and marginal cost are MB(H)= 1,300 - 40H and MC(H)= 500 + 120H.For how many hours should you schedule the worker? A) 11.25 hours B) 2.5 hours C) 5 hours D) 0 hours

Question

Quizplus · Accepted Answer

To find the optimal amount of hours to schedule the worker, we want to look for the point where MB = MC. 
1,300 - 40H = 500 + 120H
780 = 160H
H = 4.875

Since we can only schedule the worker in integer increments, we round down to the nearest integer which is 4. This means we should schedule the worker for 4 hours per day.

Note that if we were allowed to schedule the worker in non-integer increments, the optimal amount of hours would be 4.875 or 11.25 hours per day. However, since we cannot schedule the worker for a fraction of an hour, the closest integer is 4.

Suppose That You Can Schedule a Worker for Up to 4