Question

The Lost Mountains of northern Iowa are inhabited by the rare Marshallian deer. Patches of grass are far apart in this rugged land. If a deer finds a fresh patch of grass and spends h hours grazing it, it gets the square root of h units of grass. The deer compete for grass. When there are n deer, it takes a deer n 2 min- utes to find a fresh patch. A deer can survive if it gets 1 unit of grass every 200 minutes. a. Find the average cost in time of a unit of grass if a deer gets y units of grass from each patch. b. How much time will an efficient deer spend in each patch when there are n deer? (Hint: Minimize aver- age cost.) c. Since there is free entry into the deer business, the equilibrium population is the maximum number of efficient deer who can survive. How many is this?

Question A Answer is y+(n2)/y. how?

Answer 1

Answering A as only A's explanation is asked

A. To get y units of grass, the deer requires to spend y² hours grazing it. It also needs to find the patch, which itself takes n² hours. So, total time needed

y²+n²= Total cost in time

Average cost= Total cost/y

So, average cost= (y²+n²)/y= y+n²/y