Profit, Revenue, and Costs are the 3 parts of the profit function. A profit function is a wellknown concept used in the business world to determine the profit, by the revenue and costs of a business. The revenue is defined as the amount that the business collects for payment from its customers however this money must be used to pay off the business costs before it can be called a Profit. The profit function can give you a model for a business that will actually be successful. With the profit function you can find out if your costs are too high to “breakeven,” 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 is “born,” 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. Until you break even, your profit is a value in negative numbers even though you have revenue.
Business Math question
Max, 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 he sells that includes the labor (paying employee) 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. He sells each sandwich for $5.50 so the Revenue of the business is 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?
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 their revenue make a profit however they still must pay their ongoing daily costs out of the revenue before they can count a profit.
Costs: For the business owner, the minimum wage might be bundled into the variable costs of the business under “Labor and materials” of $2.50x (per sandwich) and the fixed costs of the business (rent, utilities, insurance) are $75 per day. The costs of the business in the profit function are represented by C(x).
An equation modeling the Costs C(x) of the 1^{st} business model would be C(x) = 2.5x+75. The Revenue R(x) is $5.50 per sandwich.The Profit P(x) of the first business model would be P(x)=R(x)C(x) which is P(x)= 5.5x (2.5x+75) which simplfies to a profit function of P(x)=3x75.
An equation modeling costs of the second business model with higher costs is C(x) = 3.5x+100. The Revenue R(x) is $6.50 per sandwich. The Profit of the second business model would be P(x)=R(x)C(x) which is P(x)= 6.5x (3.5x+100) which simplfies to a profit function of P(x)=3x100.
Revenue:
1st business model: The revenue is based on the cost of one sandwich which is $5.50. Minimum wage is $9.00 per hour.
2nd business mode: The revenue is based on the cost of one sandwich which is $6.50.* Minimum wage is $11.50 per hour.
* 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 alleviate poverty. If you raise minimum wage too much it would cause the business to go out of business.
 Andrea Boggs
