Question: Consider a firm that makes plastic cups. It produces the cups using two inputs: metal molds and plastic pellets that are melted and injected into the molds. The firm only needs one metal mold to produce any number of cups. As long as it has one mold, the firm can produce y = In(x + 1) cups when it uses x pellets. Metal molds cost $10 each and the plastic pellets cost $1 each. Find the total cost function, TC(y), and the average total cost function, ATC(y), for this firm. (This cost function is not standard: it is not like other examples we have done. However, the intuition behind it is the same: the function TC(y) should tell you the minimum possible cost of producing y units of output.)