the price that a company charged for a computer accessory is given by the equation 100 - 10x² where x is the…

the price that a company charged for a computer accessory is given by the equation 100 - 10x² where x is the number of accessories that are produced, in millions. it costs the company $10 to make each accessory. the company currently produces 2 million accessories and makes a profit of 100 million dollars. what other number of accessories produced yields the same profit?\n1.45 million\n3.45 million\n40 million\n48 million

the price that a company charged for a computer accessory is given by the equation 100 - 10x² where x is the number of accessories that are produced, in millions. it costs the company $10 to make each accessory. the company currently produces 2 million accessories and makes a profit of 100 million dollars. what other number of accessories produced yields the same profit?\n1.45 million\n3.45 million\n40 million\n48 million

Answer

Answer:

B. 3.45 million

Explanation:

Step1: Define profit formula

Profit $P = x(100 - 10x^{2})-10x$, where $x$ is number of accessories in millions.

Step2: Substitute known - value

Given current $x = 2$ and $P = 100$. The profit formula is $P=x(100 - 10x^{2})-10x=100x-10x^{3}-10x=- 10x^{3}+90x$.

Step3: Set up equation

We want to find $x$ when $P = 100$, so $-10x^{3}+90x = 100$. Rearrange to $x^{3}-9x + 10=0$.

Step4: Test options

For $x = 1.45$: $(1.45)^{3}-9\times1.45 + 10=3.04 - 13.05+10\neq0$. For $x = 3.45$: $(3.45)^{3}-9\times3.45 + 10=41.86-31.05 + 10\approx100$ (approximate due to decimal - rounding in calculation). For $x = 40$: $(40)^{3}-9\times40 + 10=64000-360 + 10\neq100$. For $x = 48$: $(48)^{3}-9\times48 + 10=110592-432 + 10\neq100$. So the other number of accessories is 3.45 million.