Question

A business owner pays $1,200 per month in rent and a total of $120 per hour in employee salary for each hour the store is open. On average, the store brings in $200 in net sales per hour.

Which equations can be solved to determine the break-even point if C(x) represents the cost function, R(x) represents the revenue function, and x the number of hours per month the store is open?

Answer 1

Let C(x) = 1200 + 120x (rent + $120 per hour) and R(x) = 200x (revenue per hour).

Solve for break-even by
- R(x) = C(x), i.e. 200x = 1200 + 120x, or
- R(x) − C(x) = 0, i.e. 200x − (1200 + 120x) = 0.

Solving 200x = 1200 + 120x gives 80x = 1200, so x = 15 hours per month.