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 patch of grass and getting y units of grass from it? (b) Find an expression for her marginal and her average costs 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 patch if she wanted to maximize her food intake? (Hint: Minimize the average cost per unit of grass eaten.)
