An important application of Mathematics is present in Economics through the Cost, Revenue and Profit Functions.
Cost Function
The cost function is related to the expenses made by a company, industry, store, in the production or acquisition of a product. The cost can have two parts: one fixed and one variable. We can represent a cost function using the following expression: C(x) = Cf + Cv, where Cf: fixed cost and Cv: variable cost
Recipe Function
The revenue function is linked to the gross sales of an entity, depending on the number of sales of a given product.
R(x) = px, where p: market price and x: number of goods sold.
Profit Function
The profit function refers to the companies' net profit, profit arising from the subtraction between the revenue function and the cost function.
L(x) = R(x) - C(x)
Example
A steel company manufactures pistons for automotive engine assemblers. The fixed monthly cost of R$ 950.00 includes electricity, water, taxes, salaries and so on. There is also a variable cost that depends on the number of pistons produced, the unit being R$ 41.00. Considering that the value of each piston on the market is equivalent to R$ 120.00, assemble the Cost, Revenue and Profit Functions. Calculate the net profit value on the sale of 1000 pistons and how many pieces, at a minimum, need to be sold in order to make a profit.
Total monthly cost function:
C(x) = 950 + 41x
Recipe Function
R(x) = 120x
Profit Function
L(x) = 120x - (950 + 41x)
Net profit in the production of 1000 pistons
L(1000) = 120*1000 – (950 + 41 * 1000)
L(1000) = 120,000 - (950 + 41000)
L(1000) = 120,000 - 950 - 41000
L(1000) = 120,000 - 41950
L(1000) = 78,050
Do not stop now... There's more after the advertising ;)
The net profit in the production of 1000 pistons will be R$ 78,050.00.
In order to make a profit, the revenue must be greater than the cost.
R(x) > C(x)
120x > 950 + 41x
120x – 41x > 950
79x > 950
x > 950 / 79
x > 12
To make a profit, you must sell over 12 pieces.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Roles - Math - Brazil School
Would you like to reference this text in a school or academic work? Look:
SILVA, Marcos Noé Pedro da. "Mathematics in Economics: Cost Function, Revenue Function and Profit Function"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/matematica-na-economia-funcao-custo-funcao-receita-.htm. Accessed on June 28, 2021.
