profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures…

profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures televisions can be modeled by the polynomial $3x^{2}+180x$. the cost, in dollars, of producing the televisions can be modeled by $3x^{2}-160x + 300$. the variable $x$ is the number of televisions sold. if 150 televisions are sold, what is the profit? $2,700 $6,000 $50,700 $51,300

profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures televisions can be modeled by the polynomial $3x^{2}+180x$. the cost, in dollars, of producing the televisions can be modeled by $3x^{2}-160x + 300$. the variable $x$ is the number of televisions sold. if 150 televisions are sold, what is the profit? $2,700 $6,000 $50,700 $51,300

Answer

Explanation:

Step1: Find the profit formula

Profit $P(x)=R(x)-C(x)$, where $R(x) = 3x^{2}+180x$ is the revenue - function and $C(x)=3x^{2}-160x + 300$ is the cost - function. $P(x)=(3x^{2}+180x)-(3x^{2}-160x + 300)$ $P(x)=3x^{2}+180x - 3x^{2}+160x-300$ $P(x)=(3x^{2}-3x^{2})+(180x + 160x)-300$ $P(x)=340x-300$

Step2: Substitute $x = 150$ into the profit formula

Substitute $x = 150$ into $P(x)=340x-300$. $P(150)=340\times150-300$ $P(150)=51000 - 300$ $P(150)=50700$

Answer:

$50,700$