Assume that the relationship between the growth of a fish population and the pop

Assume that the relationship between the growth of a fish population and the populationsize can be expressed as g = 4P 0.1P2 where g is the growth in tons and P is the size ofthe population (in thousands of tons). Given a price of $100 a ton the marginal benefitof smaller population sizes (and hence larger catches) can be computed as 20P 400.a. Compute the population size that is compatible with the maximumsustainable yield. What would be the size of the annual catch if thepopulation were to be sustained at this level?b. If the marginal cost of additional catches (expressed in terms of thepopulation size) is MC = 2(160 P) what is the population size that iscompatible with the efficient sustainable yield?