the price received for a bicycle is given by the equation b = 100 - 10x^2, where x is the number of bicycles…

the price received for a bicycle is given by the equation b = 100 - 10x^2, 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 = -10x^2 - 60x + 100 p = -10x^3 + 40x p = - 10x^2 + 40

the price received for a bicycle is given by the equation b = 100 - 10x^2, 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 = -10x^2 - 60x + 100 p = -10x^3 + 40x p = - 10x^2 + 40

Answer

Explanation:

Step1: Recall profit formula

Profit $P$ = Revenue - Cost.

Step2: Find revenue function

Revenue is price per unit times number of units. Price $b = 100 - 10x^{2}$, number of units is $x$ (in millions), so Revenue $R=(100 - 10x^{2})x=100x-10x^{3}$.

Step3: Find cost function

Cost per unit is $60$, number of units is $x$ (in millions), so Cost $C = 60x$.

Step4: Calculate profit function

$P=R - C=(100x-10x^{3})-60x=-10x^{3}+40x$.

Answer:

$P = - 10x^{3}+40x$