# Find cost revenue and profit function

• MHB
• Suraphel
In summary, the conversation discusses finding the cost, revenue, and profit functions for a new product based on different selling prices and estimated sales. The number of units sold is determined as a linear function of price, and the weekly production cost is calculated. The revenue is the product of the number of units sold and price, and profit is determined by subtracting cost from revenue. The conversation suggests determining an equation for profit in terms of price and finding the price that maximizes profit.
Suraphel
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.

Suraphel said:
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.

## What is the cost, revenue, and profit function?

The cost, revenue, and profit function is a mathematical representation of the relationship between the cost, revenue, and profit of a business. It shows how changes in the cost and revenue affect the overall profit of the business.

## How do you find the cost, revenue, and profit function?

The cost, revenue, and profit function can be found by using the cost, revenue, and profit equations, which are determined by the type of business and its operations. These equations can be derived from the business's financial statements and data.

## Why is it important to find the cost, revenue, and profit function?

It is important to find the cost, revenue, and profit function because it helps businesses make informed decisions about pricing, production, and marketing strategies. It also allows businesses to analyze their financial performance and identify areas for improvement.

## What are the variables in the cost, revenue, and profit function?

The variables in the cost, revenue, and profit function are the cost, revenue, and profit themselves. These variables can also be broken down into their individual components, such as fixed costs, variable costs, unit price, and quantity sold.

## How can the cost, revenue, and profit function be used to maximize profits?

The cost, revenue, and profit function can be used to maximize profits by analyzing the relationship between cost and revenue. By finding the optimal balance between cost and revenue, businesses can determine the most profitable price and production level for their products or services.

• General Math
Replies
2
Views
3K
• General Math
Replies
6
Views
3K
• General Math
Replies
2
Views
6K
• General Math
Replies
3
Views
2K
• General Math
Replies
1
Views
2K
• General Math
Replies
1
Views
5K
• General Math
Replies
1
Views
2K
• General Math
Replies
2
Views
4K
• General Math
Replies
1
Views
2K
• General Math
Replies
4
Views
3K