# Business MathFind cost revenue and profit function

#### Suraphel

##### New member
Dear All,
Here is my question.
The marketing department estimates that if the selling price of the new product is set 40 dollar per unit, sales will be 400 units per week. If the selling price is 20dollar per unit, sales will be 800 units per week. The production dept estimates that variable cost will be 7.5 dollar per unit and fixed cost is dollar 10000 per week. Find cost, revenue and profit function.
Kindly put the necessary step to understand. Thank in advance.

#### skeeter

##### Well-known member
MHB Math Helper
Dear All,
Here is my question.
The marketing department estimates that if the selling price of the new product is set 40 dollar per unit, sales will be 400 units per week. If the selling price is 20dollar per unit, sales will be 800 units per week. The production dept estimates that variable cost will be 7.5 dollar per unit and fixed cost is dollar 10000 per week. Find cost, revenue and profit function.
Kindly put the necessary step to understand. Thank in advance.
Number of units sold, $n$, is a function of price, $p$ ... i.e. $n = f(p)$.

You are given two data points. Represented as ordered pairs $(p,n)$ ... $(40,400)$ and $(20,800)$

From these two points, one may determine number of units sold as a linear function of price, $n = 1200-20p$

Weekly production cost would be $C = 10000 + 7.5n$

Weekly revenue from the sale of $n$ units is $R = n \cdot p$

finally, Profit = Revenue - Cost

From here, see what you can do to determine an equation for Profit in terms of price.

You should also be able to determine the price that maximizes profit.