Blog 4

Profit, Revenue and Cost Functions

The purpose of this lesson is to teach students what a Profit, Cost and Revenue function are and how they are all related. Also, I will give examples to demonstrate how they are related.

Profit Function Equation

A profit function is a function that focuses on business applications. The main purpose for a business is to sell a product or service in order to make a profit. The profit is the revenue a company brings in for selling a product or service minus the cost for producing a product or service.

*The Profit function equation is made up of two main functions: the Revenue function and the Cost function.

·      Cost Function = C(q)

·      Revenue Function = R(q)

o   “q” represents the quantity

Profit Function = R(q) – C(q)

EXAMPLE:

A hot dog stand in Miami sells hot dogs for $3 each. So, his Revenue function is R(1) = 3x. His fixed cost for maintaining his hot dog stand every day is $50 and his variable cost is $2 per hot dog sold. So, his daily Cost function is C(q) = 50 + 2x.

1) How many hot dogs does the hot dog stand need to sell in order to break even (where revenue equals cost)?

• ·         To find the breakeven point, use the Profit function and equal it to 0.

o   P(q) = R(q) – C(q) = 0

o   Now, substitute the values given above into the equation and solve.

3x = 50 + 2x

x = 50

o   So, on any given day, the hot dog stand needs to sell 50 hotdogs to breakeven. Every hot dog he sells after that he will profit 1$ per hot dog sold.

o     Below is the Revenue and Cost function graphed to graphically demonstrate the breakeven point. As you can see, the Revenue function lies beneath the Cost function up until 50 hot dogs are sold, then the Revenue function lies above the Cost function representing the hot dog stand making a profit.