A third brother, Rex Carr, owns a junk yard. Rex can use one of two methods to destroy cars. The first involves purchasing a hydraulic car smasher that costs $200 a year to own and then spending $1 for every car smashed into oblivion; the second method involves purchasing a shovel that will last one year and costs $10 and paying the last Carr brother, Scoop, to bury the cars at a cost of $5 each.
(a) Write down the total cost functions for the two methods, where y is output per year: TC1(y) = _______, TC2(y) = _______.
(b) The first method has an average cost function 1+200/y and a marginal cost function _______. For the second method these costs are _______ and _______.
(c) If Rex wrecks 40 cars per year, which method should he use? _______. If Rex wrecks 50 cars per year, which method should he use? _______. What is the smallest number of cars per year for which it would pay him to buy the hydraulic smasher? _______.