A manufacturer decides to sell products at a per-unit price of $150. The per-unit material cost was $50 a year ago when the material cost index was 100. The current material cost index is 125. The products are being made by a machine that currently costs $100,000 and produces a 1000 units during its lifetime after which it needs to be replaced. The machine can be replaced by a larger one that produces proportionally larger number of units within its lifetime. However, the larger machine costs more: The power-sizing exponent for the machine cost is ½.
(a) What is the current profit (or loss) for 1000 units produced?
(b) By what factor x should a new machine be larger than the current machine so that the manufacturer can breakeven?
(c) What is the profit (or loss) for 2000 units produced if the new machine is twice the size of the current machine (i.e. when x = 2)?