Cost, Revenue and Profit Functions
Earl’s Biking Company manufactures and sells bikes. Each bike costs $40 to make, and
the company’s fixed costs are $5000. In addition, Earl knows that the price of each bike
comes from the price function Find:
1. The company’s revenue function, R(x).
2. The company’s cost function, C(x).
3. The company’s profit function, P(x).
4. The two points, (x
1
, y
1
) and (x
2
, y
2
) at which the company breaks even.
5. The output level that maximizes the company’s profit, and the maximum
profit.
1) Revenue is equal to the number of units sold times the price per unit. To obtain the
revenue function, multiply the output level by the price function.
2) A business’ costs include the fixed cost of $5000 as well as the variable cost of $40
per bike. To obtain the cost function, add fixed cost and variable cost together.
3) The profit a business makes is equal to the revenue it takes in minus what it spends
as costs. To obtain the profit function, subtract costs from revenue.
4) A company’s break-even points occur where the revenue function and the cost
function have the same value. This also implies that the profit function equals zero at
break-even points. These points are found most easily on a graphing calculator. Use the
graphing tools to plot cost and revenue functions, and find a suitable window (it may be
helpful to use ZOOM, ZOOMFIT).