Bobby, an average and unimpressive goat, grazes in a very large, mostly barren pasture with a few patches of lush grass. When he finds a new grassy area, the amount of grass he gets from it is equal to the cube root of the number of hours, h, that she spends grazing there. Finding a new patch of grass on which to graze takes him 4 hours. Since Bobby does not have pockets, the currency in which his costs are measured is time. a. What is the total cost to Bobby of finding a new plot of grass and getting y units of grass from it? b. Find an expression for his marginal costs and his average cost per patch of grass as a function of the amount of grass she gets from each patch. c. How much time would he spend in each plot if he wanted to maximize her food intake? (Hint: Minimize average costs per unit of grass eaten.)