Q8. 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 multiplier, l?