# The solution to Profit Maximization

The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past date, the following production schedule was developed:

Crew Size Amount of Fish Caught

(Number of Workers) Per Week (Hundreds of lbs.)

2 3

3 6

4 11

5 19

6 24

7 28

8 31

9 33

10 34

11 34

12 33

a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?

b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?

c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per person?

d. Suppose the owner of the trawler can sell al the fish caught for $75 per 100 pounds and can hire a many crew members as desired by paying them $150 per week. Assuming that the owner of the trawler is interested in maximizing profits, determine the optimal crew size.

#### Solution Summary

This posting examines profit maximization.