the revenue, in dollars, of a company that produces video game systems can be modeled by the expression…

the 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 $

the 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: Find the profit expression

Profit (P=\text{Revenue}-\text{Cost}). Given Revenue (R = 5x^{2}+2x - 80) and Cost (C=5x^{2}-x + 100). [ \begin{align*} P&=(5x^{2}+2x - 80)-(5x^{2}-x + 100)\ &=5x^{2}+2x - 80-5x^{2}+x - 100 \end{align*} ]

Step2: Combine like - terms

Combine the (x^{2}) terms ((5x^{2}-5x^{2} = 0)), the (x) terms ((2x+x=3x)), and the constant terms ((-80 - 100=-180)). So, (P = 3x-180).

Step3: Calculate the profit when (x = 1000)

Substitute (x = 1000) into the profit formula (P=3x-180). (P=3\times1000-180). [ \begin{align*} P&=3000-180\ &=2820 \end{align*} ]

Answer:

The profit expression is (3x - 180). When (x = 1000), the profit is ($2820).