$4.$ Precious Bar is a small town tavern that sells only bottled beer. The average price of a bottle of beer is $$4\mathrm{.}00$ and the average cost of a bottle of beer is $$1\mathrm{.}50.$ Precious$$ bar is open at night. One bartender and $2-3$ servers work each night. The fixed costs $($salaries$,$ rent, tax and utilities etc.$)$ total $$250,000$ per year.

a$)$ Precious wants to know how many bottles of beer his bar must sell during the year to start making a profit? $(1$ marks$)$

b$)$ What is the revenue at the break$-$even quantity found in part A$.?(1$ mark$)$

c$)$Precious want to make $$100,000$ a year as an annual profit. How many bottles of beer should his bar need to sell to make a $$100,000$ profit? $(2$ marks$)$