Calculating Total Profit for The Scooter Company's Electric Scooter Sales

By keeping a close eye on these metrics, The Scooter Company can make data-driven decisions that promote sustainability and growth in the competitive electric scooter market.nderstanding the financial fundamentals of manufacturing and selling products is vital for any business. In the case of The Scooter Company, which specializes in the production and sales of electric scooters, determining the total profit function is essential for strategic planning and financial analysis.

When analyzing The Scooter Company's profitability, we must consider both variable and fixed costs, as well as the revenue generated by sales. The cost to produce each electric scooter is $150, and there is a fixed cost of $2,000 that the company incurs, regardless of the number of scooters sold. Revenue, on the other hand, is the income generated from scooter sales and is provided by the function r(x) = 400x − 2x², where x represents the number of electric scooters sold.

To calculate the total profit function, we need to subtract the total cost from the total revenue. The total cost function combines the fixed cost and the variable cost per unit multiplied by the number of units sold, which can be expressed as c(x) = 2000 + 150x. The profit function, denoted as p(x), is the difference between the revenue function r(x) and the cost function c(x).

Therefore, the profit function for The Scooter Company is:

p(x) = r(x) − c(x)
= (400x − 2x²) − (2000 + 150x)
= 400x - 2x² - 2000 - 150x
= 250x - 2x² - 2000

This function, p(x) = 250x - 2x² - 2000, represents the total profit depending on the number of scooters sold, which is a key indicator for The Scooter Company’s financial performance.

For businesses and financial enthusiasts, understanding such profit functions provides insights into the break-even point, optimal pricing strategies, and sales targets necessary to achieve desired profit margins. By keeping a close eye on these metrics, The Scooter Company can make data-driven decisions that promote sustainability and growth in the competitive electric scooter market.