Consider a project to supply Detroit with $27,000$ tons of machine screws annually for automobile production. You will need an initial $$5,600,000$ investment in threading equipment to get the project started; the project will last for $6$ years. The accounting department estimates that annual fixed costs will be $$1,350,000$ and that variable costs should be $$255$ per ton; accounting will depreciate the initial fixed asset investment straight$-$line to zero over the $6-$year project life. It$.$ also estimates a salvage value of $$725,000$ after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $$368$ per ton. The engineering department estimates you will need an initial net working capital investment of $$540,000.$ You require a return of $12$ percent and face a tax rate of $23$ percent on this project.

a$.$ Suppose you're confident about your own projections, but you're a little unsure ab 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$.,32)$

$\backslash$table$[[$a$.\frac{?}{{?}_{\frac{?}{?}}OC}\frac{F}{\frac{?}{{?}_{\frac{?}{?}}}}Q,$$$,87\mathrm{.}01],[$b$.\frac{?}{{?}_{\frac{?}{?}}NP}\frac{V}{\frac{?}{{?}_{\frac{?}{?}}}}Q,$$$,357\mathrm{.}73],[$c$.$ Minimum level of output,,$0]]$