the revenue, in dollars, of a company that produces jeans can be modeled by 2x²+17x - 175. the cost, in…

the revenue, in dollars, of a company that produces jeans can be modeled by 2x²+17x - 175. the cost, in dollars, of producing the jeans can be modeled by 2x² - 3x - 125. the number of pairs of jeans that have been sold is represented by x. if the profit is the difference between the revenue and the cost, which expression can be used to find profit and what is that profit when 75 pairs of jeans are sold?\n20x - 50; $500\n20x - 50; $1,450\n20x + 50; $1,550\n20x + 50; $5,250
Answer
Explanation:
Step1: Find profit expression
Profit $P$ = Revenue - Cost. Given Revenue $R = 2x^{2}+17x - 175$ and Cost $C=2x^{2}-3x - 125$. Then $P=(2x^{2}+17x - 175)-(2x^{2}-3x - 125)$. [ \begin{align*} P&=2x^{2}+17x - 175 - 2x^{2}+3x + 125\ &=(2x^{2}-2x^{2})+(17x + 3x)+(-175 + 125)\ &=20x-50 \end{align*} ]
Step2: Calculate profit when $x = 75$
Substitute $x = 75$ into the profit - expression $P = 20x-50$. $P=20\times75-50$. $P = 1500-50=1450$.
Answer:
20x - 50; $1,450