$13.$ Taylor runs her own hot dog stand. The monthly cost of the cart rental and business permit is $$300.$ Rachel spends $$0\mathrm{.}50$ on each hot dog sold, including bun and condiments. She sells each hot dog for $$2\mathrm{.}00,$

$1)$ What is the contribution margin per unit?

$2)$ What the contribution margin ratio?

$3)$ Predict operating income for a month in which Taylor sells $1,000$ hot dogs.

$4)$ How many hot dogs does Taylor need to sell each month to breakeven?

$5)$ How much sales revenues doe Taylor need to generate each month to breakeven?

$6)$ How many hot dogs does Taylor need to sell each month to earn a target profit of $$900$ a month?

$7)$ How much sales revenue does Taylor need to generate each month to earn a target profit of $$900$ per month?