Question

Break Even Analysis for Small Business 1) Jesse wants to start a business making and selling skateboards. She will charge $75 for each one. Her cost will be $30 per skateboard for materials. She must pay $500 per month rent (which includes utilities) so that she has a place to make and sell the skateboards. a) Write a rule for her revenue (money coming in). b) Write a rule for her cost.​

Answer 1

a) r(b) = 75b

b) c(b) = 30b +500

Explanation:

Revenue is the product of the selling price per unit and the number of units. The cost will be the sum of fixed (overhead) cost and production cost per unit multiplied by the number of units produced.

__

Let b represent the number of skateboards Jesse produces in a month.

a)

Jesse receives $75 for each skateboard sold. Her revenue from selling 'b' skateboards is ...

r(b) = 75b

__

b)

It costs Jesse $30 for each skateboard produced, and $500 for overhead. Her total cost is ...

c(b) = 30b +500

_____

Additional comment

In order to break even, Jesse's revenue must equal her cost:

75b = 30b +500

45b = 500

b = 11 1/9

Jesse must produce and sell 12 skateboards each month to cover her costs. (In a real business, there are additional considerations related to inventory, shrinkage, returns, discounts, and other things that may increase cost or reduce revenue.) After covering costs, each additional skateboard sold will give Jesse a profit of $45.