In a particular region, there are two lakes rich in fish. The quantity of fish caught in each lake depends on the number of persons who fish in each, according to Q1 = 10N1 -.1N12 and Q2 = 16N2 -.4N22, where N1 and N2 denote the number of fishers at each lake. In all, there are 40 fishers.
a. Suppose N1 = 16 and N2 = 24. At which lake is the average catch per fisher greater? In light of this fact, how would you expect the fishers to re-deploy themselves?
b. How many fishers will settle at each lake? (Find N1 and N2 such that the average catch is equal between the lakes.)
c. The commissioner of fisheries seeks a division of fishers that will maximize the total catch at the two lakes. Explain how he should use information on the marginal catch at each lake to accomplish this goal. What division of the 40 fishers would you recommend?