Calculating Profit: Understanding The Scooter Company's Financials

Understanding how to leverage this profit function can ultimately guide the company towards a profitable and sustainable future in the competitive electric scooter market.nderstanding how to leverage this profit function can ultimately guide the company towards a profitable and sustainable future in the competitive electric scooter market.avigating through the financial aspects of manufacturing can be intricate, especially for businesses like The Scooter Company that produce electric scooters. A critical piece of understanding these finances comes in the form of calculating the total profit of the company. For those invested in the economics of scooter manufacturing, grasping the profit calculation is essential to assess the company's financial health and sustainability.

Breaking Down the Costs

Each electric scooter incurs a production cost of $200. Alongside variable costs, The Scooter Company tackles a steady fixed cost of $1,500, which covers expenses such as rent, utilities, and salaried personnel that remain constant regardless of the output levels.

Understanding Revenue

The total revenue (R) for The Scooter Company is determined by the function R(x) = 300x - 3x^2, where x denotes the number of electric scooters sold. This quadratic revenue function suggests that the company experiences increasing revenue up to a certain point, beyond which revenue begins decreasing due to the quadratic term that implies the effect of diminishing returns or market saturation.

Deriving the Profit Function

Profit is calculated by subtracting the total costs from the total revenue. In the case of The Scooter Company, we need to consider both variable costs (associated with producing each electric scooter) and the fixed costs.

The variable cost for each scooter is $200, so this would give us a function V(x) = 200x. Adding the fixed cost of $1,500 gives the total cost function C(x) = V(x) + 1500 = 200x + 1500.

To derive the profit function, subtract the total cost function from the total revenue function:

P(x) = R(x) - C(x)
     = (300x - 3x^2) - (200x + 1500)
     = 300x - 3x^2 - 200x - 1500
     = 100x - 3x^2 - 1500

This simplifies to P(x) = -3x^2 + 100x - 1500. The function P(x) represents The Scooter Company's total profit based on the number of scooters sold and highlights the interplay between production costs, sales, and revenue.

Conclusion

The total profit function is a crucial metric for The Scooter Company. It allows the business to calculate its break-even point, to strategize pricing, and to forecast the financial outcomes based on different sales volumes. Understanding how to leverage this profit function can ultimately guide the company towards a profitable and sustainable future in the competitive electric scooter market.