Calculating Profit for Electric Scooter Sales: Understanding the Scooter Company's Revenue and Costs

Electric scooters have gained popularity as eco-friendly transportation options, and as more consumers opt for these convenient rides, understanding the financial aspects behind their production and sales is crucial for companies like The Scooter Company. For those interested in the economics of manufacturing electric scooters, it's important to grasp how revenue and production costs affect overall profit. The Scooter Company's profit model can be broken down into variable and fixed costs, with a revenue function that reflects sales performance.

Understanding Costs and Revenue

The production cost for each electric scooter is $200, which represents the variable cost per unit. Additionally, there is a fixed cost totaling $1,500, which the company must cover regardless of the number of scooters sold. To conceptualize total revenue, The Scooter Company employs the function $r(x) = 400x - 2x^2$, where $x$ signifies the number of scooters sold.

Deriving the Profit Function

Profit is calculated by subtracting the total costs from the total revenue. Therefore, the profit function for The Scooter Company incorporates both variable and fixed costs and is derived as follows:

• Revenue function: $r(x) = 400x - 2x^2$


• Variable cost per scooter: $200x$


• Fixed cost: $1,500$

Given that the total cost (TC) is the sum of variable costs and fixed costs we have: $TC(x) = 200x + 1,500$.

The profit function (P) is the difference between the revenue function and total costs:

$$P(x) = r(x) - TC(x)$$
$$P(x) = (400x - 2x^2) - (200x + 1,500)$$
$$P(x) = -2x^2 + 200x - 1,500$$

Therefore, the correct profit function that represents The Scooter Company's total profit is -2x^2 + 200x - 1,500.

Understanding this function is vital for The Scooter Company to plan their production, set sales targets, and forecast profits effectively.

Conclusion

In conclusion, the company's total profit function is essential for predicting financial outcomes and making informed business decisions. With a clear profit model, electric scooter companies can navigate the competitive market and drive towards profitability and growth.