Consider the owners of a small lawn-mowing service. They can use one of two methods to mow lawns. Method 1 is to purchase a tractor that costs $200 a year to own and then spend $1 (for labor and gas) for every acre of grass cut. Method 2 is to spend $40 on a used push mower that will last one year and then spend $5 (for labor) for every acre of grass cut.

a. prepare down the total cost functions for the two methods, letting q represent the number of acres of grass cut per year. (In other words, find an equation with total cost or C on the left-hand side and q on the right-hand side for both methods.)

b. Find the average total cost function and the marginal cost for each of the two methods. (Here, find an equation with ATC on the left-hand side and q on the right-hand side for each method. For MC, you do not need an equation. You will have a single dollar value for each method.)

c. Assume that the tractor and the push mower have no resale value at the end of the year. What is the smallest number of acres of grass cut per year for which the owners should buy the tractor? Show work.