Charles McCoy is a manager at a coffee shop and is making hiring decisions. With one worker, he can make 15 drinks that sell for $3 on average in a single hour. With a second worker, he can make an additional 12 drinks in a single hour. The marginal benefit of each additional worker decreases by three drinks with each additional hire. Assuming that workers are paid $12 per hour and work eight hours, how many employees should Charles hire for each hour?
A)Three
B)Four
C)Five
D)Six

Question

Quizplus · Accepted Answer

The first worker can produce 15 drinks per hour, which translates to $45 of revenue per hour (15 x $3). If the cost of hiring this worker is $12, then the net benefit is $33 per hour.

The second worker can produce an additional 12 drinks, bringing the total to 27 drinks per hour. This translates to $81 of revenue per hour. However, the cost of hiring the second worker is $24 (2 x $12), so the net benefit is only $57 per hour.

The marginal benefit of hiring a third worker is only 9 drinks (down from 12), which translates to $27 of revenue per hour. The cost of the third worker is $36 (3 x $12), so the net benefit is only $21 per hour.

Continuing this pattern, we can calculate the net benefit of each additional worker:

- Fourth worker: 6 drinks, $18 of revenue, and a net benefit of $6
- Fifth worker: 3 drinks, $9 of revenue, and a net benefit of -$3 (i.e. a net loss)
- Sixth worker: 0 additional drinks and a net loss of $12 (i.e. the cost of the worker)

Therefore, the optimal number of workers for each hour is four.

Charles McCoy Is a Manager at a Coffee Shop and Is