Question

The Scooter Company manufactures and sells electric scooters. Each scooter cost $200 to produce, and the company has a fixed cost of $1,500. The Scooter Company earns a total revenue that can be determined by the function R(x) = 300x − 3x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?

Answer 1

Answer:

-3x^2+100x-1500

Step-by-step explanation:

Create an equation for the total cost.

1500+200x

1500 is the fixed cost, plus the additional 200 it costs to create a scooter.

Then you need to subtract that from the revenue, which is provided in a function. 300x-3x^2

[300x-3x^2] - [1500+200x]

Solve.

100x - 3x^2 -1500

Write in standard form.

-3x^2+100x-1500

Answer 2

Total profit of a company is the difference between total revenue and total cost.

The Scooter Company's total profit function is represented by -3x² + 100x - 1500

Given:

Cost of each scooter = $200

Number of scooter sold = x

Fixed cost = $1,500

• Variable cost = Cost of each scooter × Number of scooter sold

Total cost = fixed cost + variable cost

= 1,500 + (200 × x)

= 1500 + 200x

• Cost, C(x) = 1500 + 200x

• Revenue,R(x) = 300x − 3x²

Total profit = Revenue - Cost

= (300x − 3x²) - (1500 + 200x)

= 300x - 3x² - 1500 - 200x

= -3x² + 100x - 1500

Therefore, the Scooter Company's total profit function is represented by -3x² + 100x - 1500

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