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 = 15 N1- 0.5 N12 and Q2 = 8 N2 - 0.2 N22

where N1 and N2 denote the # of fishers at each lake.

In all there are 28 fishers, i.e. N1 + N2 = 28.

(a) Suppose N1 = 16 and N2 = 12. At which lake is the average catch per fisher greater? In light of this fact, how would you expect the fishers to redeploy themselves?

(b) How many fishers will settle at each lake?

(c) The Department of Fisheries seeks a division of fishers that will maximize the total catch at the two lakes. What division of the 28 fishers would you recommend to the Department?

(d) What interpretation would you give to the Lagrangian multiplie, λ?