Haya is considering a business venture$-$selling custom$-$embroidered T$-$shirts from a pushcart kiosk at University Market. The T$-$shirts will be available in $12$ different colors and one$-$size fits all. The T$-$shirts$$ unique feature is that almost any name, phrase, or logo$,$ can be stitched onto the T$-$shirt while the customer waits. Thus, a customer can obtain a T$-$shirt with his or her own name, special saying, or favorite logo in a wide variety of thread colors, sizes, and fonts. Based on preliminary market research and input from the franchising company, Haya plans on selling each embroidered T$-$shirt for $$20.$

Haya plans to acquire the necessary technology by obtaining a franchise from KM Company. KM Company sells all of the necessary equipment and technology and provides the inventory of T$-$shirts and other supplies. In addition, KM Company trains prospective franchisees such a Haya in the basics of running the business and operating the machines.

Haya will need to buy the T$-$shirts from KM Company for $$4$ per T$-$shirt and pay a royalty to the franchising company of $$2$ per T$-$shirt sold. In addition, Haya believes that each T$-$shirt will use about $$2\mathrm{.}50$ worth of supplies $($including thread, replacement of sewing needles, machine maintenance, etc.$).$ Finally, KM Company requires that each franchisee invest $$250$ per month on leaflets and brochures to advertise the product.

Haya discovers that University Market would supply her with the pushcart and all of the necessary equipment for proper display. The license from the Market also allows Haya to use electrical outlets and two telephone outlets. University Market will pay for Haya$$s electricity consumption, but she will have to obtain two business telephone lines at a cost of $$50$ per line per month. University Market is willing to license the space and equipment to Haya on a monthly basis for $$1,970$ per month.

To generate maximum sales, Haya wants to keep the pushcart open for business from $10$ A$.$M$.$ to $10$ P$.$M$.$ Monday through Friday, and from $10$ A$.$M$.$ to $6$ P$.$M$.$ on Saturday and Sunday. Haya is willing to put in $50$ hours at the kiosk, and she can obtain additional part$-$time help at $$10$ per hour $($only one individual is required to operate the business$).$ Haya$$s only other significant expense is setting up to accept credit cards. Haya anticipates that $75\%$ of her sales will be credit card sales, and the credit card company charges Haya a fee of $2\%$ of the selling price.

Required:

a$.$ Write down the expression for Haya$$s monthly profit. $($Assume that there are exactly $4$ weeks per month$)?$

b$.$ Calculate Haya$$s monthly breakeven point in T$-$shirts. What does this translate to in revenue?

c$.$ How much profit would Haya earn in a month if she sold $1,000$ T$-$shirts? How many T$-$shirts would Haya have to sell to earn a target profit of $$4,032$ per month?

d$.$ Haya just remembered that she did not include taxes. How will that affect part $($C$).$

e$.$ What do you think of Haya$$s business$$venture$?$