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

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? $p=-10x^{2}-60x + 100$ $p=-10x^{2}+40$ $p=-10x^{3}+40x$

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? $p=-10x^{2}-60x + 100$ $p=-10x^{2}+40$ $p=-10x^{3}+40x$

Answer

Explanation:

Step1: Recall profit formula

Profit $P$ = Revenue - Cost.

Step2: Calculate revenue

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

Step3: Calculate cost

Cost per unit is $60$, and 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:

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