Question

the price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions. it costs the company $60 to make each bicycle. what is the profit function for the company? p = –10x2 – 60x 100 p = –10x3 40x p = – 10x2 40

Answer 1

The profit function for the company is P = -10x^³ + 40x, which is derived by subtracting the total cost of production from the total revenue generated from sales.

Step-by-step explanation:

The student is asking how to determine the profit function for a company that produces bicycles. The revenue from the sale of each bicycle is given by the equation b = 100 - 10x², where x is the number of bicycles produced in millions, and the cost to produce each bicycle is $60. To find the profit function, we need to subtract the total cost from the total revenue.

Total revenue (TR) is the selling price per unit multiplied by the number of units sold, given by TR = b × x. Total cost (TC) is the cost per unit multiplied by the number of units, given by TC = 60 × x. The profit(P) is TR - TC, which when we substitute the given expressions, yields: P = (100 - 10x²) × x - 60 × x.

Expanding this we get P = 100x - 10x^3 - 60x. Further simplifying, we combine like terms to arrive at the profit function: P = -10x³+ 40x.

Answer 2

P = –10x3 + 40x