Profit, Revenue, and Costs are the 3 parts of the profit function. Revenue is defined as the money that a business collects from its customers. Profit is equal to the revenue minus the business costs. The profit function can give a business owner an idea of how many items or services they need to sell in a day in order to be profitable. With the profit function you can find out if your costs are too high to “break-even,” and how many sales of your product or service you need to have a daily profit of a certain level.
### Breaking Even

Breaking even is the concept that defines when your profit begins because when you start a business, you need to sell enough just to pay off the initial costs of the business which are higher than they will be once the business is up and running. For example, perhaps you have to pay back investors who gave you the capital to start the business? You can’t start paying them back until you are making a revenue that is higher than your costs.
### Business Math problem

Maxine, a business owner of a deli has fixed costs of $75 per day for rent, utilities and insurance and variable costs of $2.50 per sandwich she sells and that includes the labor (paying employees) and material (bread, veggies, etc). Together these amounts are the daily costs of the business and the costs can be modeled by the equation: C(x) = 2.5x + 75. She sells each sandwich for $5.50 so the revenue of the business can be modeled by the equation R(x) = $5.50x. If the Daily profit at the Deli varies between $60 and $130, then between what levels (a high and a low number) in sandwich sales do the daily sandwich sales vary? This question is asking what is the easiest way to figure out how many sandwiches the Deli is selling per day if the daily Profit is between $60 and $130 in sandwich sales? Solve the Math Problem
### Profit:

The profit will be a positive number after the revenue (sales made) exceeds the costs of running the business (rental space, buying materials, paying employees). The business breaks even at the point where the business sales go from being negative to positive because the costs of starting the business are finally paid off. This means that since the business has paid back the costs of getting the business started now they can begin seeing a profit however they still have to pay their ongoing daily costs out of the revenue before they can consider it a profit.
#### Posted: August 3, 2014

The costs of the business in the profit function are represented by C(x). An equation modeling the Costs C(x) of the business model with a lower minimum wage would be C(x) = 2.5x+75.

If P(x) = R(x) - C(x) then for the first business model where sandwiches are sold for $5.50, P(x)= 5.5x - (2.5x+75) which simplfies to P(x)=3x-75. Solve

An equation modeling costs of the second business model with a higher minimum wage is C(x) = 3.5x+100 because P(x)= 6.5x- (3.5x+100) which simplfies to P(x)=3x-100. Solve

In the first business model minimum wage is $9.00 per hour and a sandwich costs $5.50. See how the problem is solved.

In the second business model minimum wage is $11.50 per hour and a sandwich costs $6.50. See how the problem is solved.

The price of the sandwich is raised to be able to pay the employees the higher minimum wage, however this also makes the sandwich unaffordable and will hurt sales which is the main reason why raising minimum wage does not reduce poverty. If you raise minimum wage too much it would cause the business to go out of business.

By Andrea Boggs