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 profit formula

Profit $P(x)=$ Revenue $R(x)-$ Cost $C(x)$. Given $R(x)=3x^{2}+180x$ and $C(x)=3x^{2}-160x + 300$. Then $P(x)=(3x^{2}+180x)-(3x^{2}-160x + 300)$. Simplify the expression: [ \begin{align*} P(x)&=3x^{2}+180x - 3x^{2}+160x-300\ &=(3x^{2}-3x^{2})+(180x + 160x)-300\ &=340x-300 \end{align*} ]

Step2: Calculate profit for $x = 150$

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

Answer:

$50,700$