Question

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.)

Answer 1

The answer and procedures of the exercise are attached in the following archives.

Explanation

You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.