The technique for calculating a bid price can be extended to many other types of problems. Answer the following questions using the same technique as setting a bid price; that is$,$ set the project NPV to zero and solve for the variable in question. Guthrie Enterprises needs someone to supply it with $144,000$ cartons of machine screws per year to support its manufacturing needs over the next five years, and you've decided to bid on the contract. It will cost $$1,840,000$ to install the equipment necessary to start production; you'll depreciate this cost straight$-$line to zero over the project's life. You estimate that in five years this equipment can be salvaged for $$154,000.$ Your fixed production costs will be $$269,000$ per year, and your variable production costs should be $$9\mathrm{.}80$ per carton. You also need an initial investment in net working capital of $$134,000.$ The tax rate is $24$ percent and you require a return of $12$ percent on your investment. Assume that the price per carton is $$16\mathrm{.}40.$

a$.$ Calculate the project NPV$.($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the minimum number of cartons per year that can be supplied and still break even? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$

c$.$ What is the highest fixed costs that could be incurred and still break even? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$