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 3x² + 180x. the cost, in dollars, of producing the televisions can be modeled by 3x² - 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 3x² + 180x. the cost, in dollars, of producing the televisions can be modeled by 3x² - 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: Define profit formula

Profit $P(x)=R(x)-C(x)$, where $R(x) = 3x^{2}+180x$ and $C(x)=3x^{2}-160x + 300$.

Step2: Substitute revenue and cost functions

$P(x)=(3x^{2}+180x)-(3x^{2}-160x + 300)$. Expand the right - hand side: $P(x)=3x^{2}+180x - 3x^{2}+160x-300$. Combine like terms: $P(x)=(3x^{2}-3x^{2})+(180x + 160x)-300=340x-300$.

Step3: Substitute $x = 150$

Substitute $x = 150$ into the profit function $P(x)$: $P(150)=340\times150-300$. First, calculate $340\times150 = 51000$. Then, $P(150)=51000-300=50700$.

Answer:

$50,700$