Consider a project to supply Detroit with $20,000$ tons of machine screws annually for automobile production. You will need an initial $$3\mathrm{.}1$ million investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be $$925,000$ and that variable costs should be $$185$ per ton; accounting will depreciate the initial fixed asset investment straight$-$line to zero over the five$-$year project life. It also estimates a salvage value of $$400,000$ after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $$295$ per ton. The engineering department estimates you will need an initial net working capital investment of $$380,000.$ You require a return of $13$ percent and face a tax rate of $22$ percent on this project.

a$.$ Suppose you$$re confident about your own projections, but you$$re a little unsure about Detroit$$s actual machine screw requirement. What is the sensitivity of the project OCF to changes in the quantity supplied? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the sensitivity of NPV to changes in quantity supplied? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ Given the sensitivity number you calculated, what is the minimum level of output below which you wouldn$$t want to operate? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$