Hildegard, an intelligent and charming Holstein cow, grazes in a very large, mostly barren pasture with a few patches of lush grass. When she finds a new grassy area, the amount of grass she gets from it is equal to the square root of the number of hours, h, that she spends grazing there. Finding a new patch of grass on which to graze takes her 1 hour. Since Hildegard does not have pockets, the currency in which her costs are measured is time.
a. What is the total cost to Hildegard of finding a new plot of grass and getting y units of grass from it?
b. Find an expression for her marginal costs and her average cost per patch of grass as a function of the
amount of grass she gets from each patch.
c. How much time would she spend in each plot if she wanted to maximize her food intake? (Hint: Minimize
average costs per unit of grass eaten.)