Jada's Juice

Jada is planning a lemonade stand $-$ probably the most ubiquitous example of a small business, so let's start there. She'll work during weekdays and Saturdays during the summer $($June through August, and we can assume $4$ weeks per month$).$ She expects to sell $250$ cups per day and plans to charge $$8$ per cup, but she knows that for every $25-$cent increase in price, she will sell $15$ fewer cups per day. She also knows that cups will cost $$\frac{50}{?}$ pack, where each pack contains $100$ cups. Buying a table and coolers will cost her $$100.$

Did we mention that this is not ordinary lemonade? These aren't even soft drinks, and there's a shot of alcohol in every drink $-$ that's why these start at $$8$ per cup and have a real kick. So Jada needs a liquor license, which costs $$450$ per month. The juice costs her $20$ cents per cup and the alcohol costs her $$3$ per cup.

Please develop an income statement and model for Jada that will help you answer the following questions for the entire summer:

A$)$ How much does an increase in price from $$8$ to $$9\mathrm{.}50$ change profit? $($Does it go up or down? By how much?$)$

B$)$ What is Jada's profit if she charges $$12$ per drink?

C$)$ Assuming Jada is selling her drink for $$10,$ how much does an increase in alcohol from $$1\mathrm{.}00$ per cup to $$1\mathrm{.}20$ per cup change her profit? $($Does it go up or down? By how much?$)$

D$)$ What are Jada's total fixed expenses for the summer?

E$)$ If Jada charges an astronomical $$14$ for a drink, what would be her largest expense for the summer? Write the letter of the correct choice.

a$)$ total alcohol cost

b$)$ total fixed cost

c$)$ liquor license cost

d$)$ vendor permit

e$)$ cart rental