The quantity of fish in a lake grows according to the equation:

Gt = St * (100 - St)

100 , where St is the stock of fish at the beginning of period t and Gt is the amount of fish that grow during period t, both measured in tons.

a. Suppose that in a certain year, the stock of fish in the lake is equal to 20 tons.

Furthermore, both the stock of fish and the size of the harvest have been constant for a long period of time. How big is the annual harvest of fish, Ht?

b. Calculate the optimal stock of fish in the lake and the maximum sustainable yield. You can do this either by trial and error or by using calculus.