Determining Profit Function for The Scooter Company's Electric Scooters

By leveraging this critical piece of information, The Scooter Company can stride forward confidently in the competitive electric scooter market.nderstanding the financials of a manufacturing business is crucial, especially when it comes to profitability. For The Scooter Company, which specializes in electric scooters, pinpointing the profit function is key to measuring success. With a clear picture, the company can make better-informed decisions to maximize efficiency and profitability.

First, let's dive into the cost structure. The Scooter Company has a fixed cost of $1,500. Fixed costs refer to expenses that do not change with the number of units produced. In addition to fixed costs, each electric scooter incurs a variable cost of $200 to produce. This means that with every scooter made, the company spends $200.

The total revenue function is given by $R(x) = 300x - 3x^2$, where $x$ is the number of scooters sold. Revenue functions are vital as they show the earnings a company makes before any costs are deducted.

To find the profit function, we need to subtract the total cost from the total revenue. The total cost function ($TC$) combines both the variable and fixed costs and is computed as $TC(x) = 200x + 1,500$.

The profit function, therefore, is the revenue function minus the total cost function:

$Profit(x) = R(x) - TC(x)$
$Profit(x) = (300x - 3x^2) - (200x + 1,500)$

After simplifying, we get:
$Profit(x) = -3x^2 + 100x - 1,500$

This function outlines how profit varies with the number of electric scooters sold. By analyzing this function, The Scooter Company can determine the number of scooters that need to be sold to break even or achieve a certain profit level.

Understanding the profit function is essential for The Scooter Company as it provides valuable insights into their business operations. This knowledge allows them to price their electric scooters competitively while ensuring sustainable business growth. Moreover, by regularly reviewing and analyzing the profit function, the company can make agile decisions to adapt to market changes and consumer demand.

In summary, the profit function representing The Scooter Company's total profit, based on their given costs and revenue, is $-3x^2 + 100x - 1,500$. By leveraging this critical piece of information, The Scooter Company can stride forward confidently in the competitive electric scooter market.