Fanatics is spending $$3\mathrm{.}50$ each to manufacture $100,000$ jerseys in preparation for the upcoming World Series. They took out a loan at $4\mathrm{.}5\%$ in order to have the funds needed to manufacture these jerseys. They also pay $$5,000$ in warehouse rent, $$1,000$ in inventory insurance, and expect $$600$ worth of inventory to be damaged. Assume that Fanatics DOES receive the income deduction tax break for interest payments, and is taxed at the $40\%$ corporate tax rate. It took Fanatics $5$ orders to receive all the materials needed to produce their $100,000$ jerseys, and each order cost them $$1,000$ in shipping and handling.

a$)$ Find the cost Fanatics spent to manufacture the $100,000$ jerseys.

b$)$ Find the $C$ value in our total carrying cost formula.

c$)$ Find Fanatics' Total Carrying Cost, assuming they are storing inventory for exactly $1$ year before selling.

d$)$ Find Fanatics' Total Ordering Cost for all $100,000$ jerseys.

e$)$ What is the total running inventory cost for Fanatics $-$ them carrying the jerseys for $1$ year and ordering the jerseys?

f$)$ What is the total cost for the jerseys when taking all this into account $-$ their total manufacturing costs, their carrying cost for $1$ year, and their ordering costs?

g$)$ Bonus $+1!$ What price would Fanatics need to sell each jersey at in order to break even on their total jersey costs?