Sunshine's Organic Market sells organic produce. Assume that labor is the only input that varies for the firm. The store manager has determined that if she hires 12 workers, the store can sell 300 pounds of produce per day. If she hires 13 workers, the store can sell 370 pounds of produce per day. The store earns $4 for each pound of produce that it sells, and the manager pays each worker $80 per day. Assuming no changes in either the daily wages paid to store workers or the price at which the store sells its produce, what is the minimum number of sales that would allow the firm to increase its profits by hiring a 14th worker?

Question

Quizplus · Accepted Answer

First, we need to find the total revenue and the total cost for each of the given number of workers:

For 12 workers:
Total revenue = 300 pounds/day x $4/pound = $1,200/day
Total cost = 12 workers x $80/worker = $960/day
Profit = $240/day

For 13 workers:
Total revenue = 370 pounds/day x $4/pound = $1,480/day
Total cost = 13 workers x $80/worker = $1,040/day
Profit = $440/day

Now, we need to find the minimum number of sales required to cover the additional cost of hiring a 14th worker. The additional cost of hiring a 14th worker is $80/day.

Profit with 14 workers:
Total revenue = x pounds/day x $4/pound = $4x/day
Total cost = 14 workers x $80/worker = $1,120/day
Profit = $4x/day - $1,120/day

To cover the additional cost of hiring a 14th worker, the profit with 14 workers needs to be at least $80/day more than the profit with 13 workers. So, we can set up the following equation:

$4x/day - $1,120/day = $440/day + $80/day

Solving for x, we get x = 390 pounds/day.

Therefore, the minimum number of sales that would allow the firm to increase its profits by hiring a 14th worker is 390 pounds per day.
The correct answer is (C).

Sunshine's Organic Market Sells Organic Produce