What is the equation used to calculate the marginal revenue of the DIY-cleaner sales, and how is it applied to determine the additional revenue generated from each unit sold?
Understanding Marginal Revenue Calculation
Marginal Revenue Formula: MR = 7e^0.01x
The marginal revenue (MR) of the DIY-cleaner sales is calculated using the formula MR = 7e^0.01x, where x represents the number of sales. This formula is essential for determining the additional revenue generated from selling each additional unit of the DIY-cleaner product.
When applying this formula, the exponential term e^0.01x showcases exponential growth, with the base e being Euler's number (approximately 2.71828). As the number of sales (x) increases, the exponential term grows, leading to a higher marginal revenue calculated for each level of sales.
To find the actual marginal revenue at a specific level of sales, you substitute the given value of x into the equation MR = 7e^0.01x and calculate the result accordingly. It's important to round the answer to two decimal places for precision.
For example, if the company has 100 sales of the DIY-cleaner, you can calculate the marginal revenue as follows:
MR = 7e^0.01(100) ≈ 7e^1 ≈ 7(2.71828)^1 ≈ 7(2.71828) ≈ 19.03
Therefore, at 100 sales, the marginal revenue is approximately $19.03. This represents the additional revenue generated by selling one more unit of the DIY-cleaner at this sales level.