the profit a company makes from producing x tabletops is modeled by the equation $p(x)=480x - 2x^{2}$. for…

the profit a company makes from producing x tabletops is modeled by the equation $p(x)=480x - 2x^{2}$. for what number of tabletops does the company make a profit of $0?\n100 tabletops\n120 tabletops\n240 tabletops\n480 tabletops

the profit a company makes from producing x tabletops is modeled by the equation $p(x)=480x - 2x^{2}$. for what number of tabletops does the company make a profit of $0?\n100 tabletops\n120 tabletops\n240 tabletops\n480 tabletops

Answer

Explanation:

Step1: Set profit equation to 0

Set $P(x)=0$, so $480x - 2x^{2}=0$.

Step2: Factor out common factor

Factor out $2x$ from the left - hand side: $2x(240 - x)=0$.

Step3: Use zero - product property

If $ab = 0$, then either $a = 0$ or $b = 0$. So $2x=0$ or $240 - x=0$. For $2x=0$, we get $x = 0$. For $240 - x=0$, we solve for $x$ and get $x = 240$.

Answer:

C. 240 tabletops