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 _______ 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?