a. 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 data, the following production schedule was developed:
|
CREW SIZE (NUMBER OF WORKERS)
|
AMOUNT OF FISH CAUGHT PER WEEK (TONNES)
|
|
2
|
3
|
|
3
|
6
|
|
4
|
11
|
|
5
|
19
|
|
6
|
24
|
|
7
|
28
|
|
8
|
31
|
|
9
|
33
|
|
10
|
34
|
|
11
|
34
|
|
12
|
33
|
Over what ranges of workers are there :
- Increasing returns,
- Constant returns,
- Decreasing returns, and
- Negative returns?
ii. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?
iii. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker?
b. Consider the above question again. Suppose the owner of the trawler can sell all the fish caught for $75 per ton and can hire as 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.