modeling profit using a polynomial expression\nthe revenue, in dollars, of a company that produces video…

modeling profit using a polynomial expression\nthe revenue, in dollars, of a company that produces video game systems can be modeled by the expression $5x^{2}+2x - 80$. the cost, in dollars, of producing the video game systems can be modeled by $5x^{2}-x + 100$, where $x$ is the number of video game systems sold. if profit is the difference between the revenue and the cost, what expression represents the profit?\nprofit can be modeled by the polynomial expression \nif 1,000 video game systems are sold, the companys profit is $

modeling profit using a polynomial expression\nthe revenue, in dollars, of a company that produces video game systems can be modeled by the expression $5x^{2}+2x - 80$. the cost, in dollars, of producing the video game systems can be modeled by $5x^{2}-x + 100$, where $x$ is the number of video game systems sold. if profit is the difference between the revenue and the cost, what expression represents the profit?\nprofit can be modeled by the polynomial expression \nif 1,000 video game systems are sold, the companys profit is $

Answer

Explanation:

Step1: Define profit formula

Profit = Revenue - Cost.

Step2: Substitute given expressions

Revenue = $5x^{2}+2x - 80$, Cost = $5x^{2}-x + 100$. So, Profit=$(5x^{2}+2x - 80)-(5x^{2}-x + 100)$.

Step3: Simplify the expression

[ \begin{align*} &(5x^{2}+2x - 80)-(5x^{2}-x + 100)\ =&5x^{2}+2x - 80 - 5x^{2}+x - 100\ =&(5x^{2}-5x^{2})+(2x+x)+(-80 - 100)\ =&3x-180 \end{align*} ]

Step4: Calculate profit for $x = 1000$

Substitute $x = 1000$ into the profit - expression $3x-180$. Then Profit=$3\times1000-180$. [ \begin{align*} 3\times1000-180&=3000 - 180\ &=2820 \end{align*} ]

Answer:

Profit can be modeled by the polynomial expression $3x - 180$. If 1,000 video game systems are sold, the company's profit is $$2820$.