Question

profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures cell phones can be modeled by the polynomial $2x^{2}+55x + 10$. the cost, in dollars, of producing the cell phones can be modeled by $2x^{2}-15x - 40$. the variable $x$ represents the number of cell phones sold. what expression represents the profit, and what is the profit if 240 cell phones are sold? $40x - 30$; $2,400$ $40x - 30$; $9,570$ $70x + 50$; $16,850$ $70x + 50$; $28,800$

Explanation:

Step1: Find the profit expression

Profit \(P=\text{Revenue}-\text{Cost}\).
Given revenue \(R = 2x^{2}+55x + 10\) and cost \(C=2x^{2}-15x - 40\).

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Step2: Calculate the profit when \(x = 240\)

Substitute \(x = 240\) into the profit expression \(P=70x+50\).
\(P=70\times240+50\)
\(P = 16800+50=16850\)

Answer:

\(70x + 50\); \(\$16,850\) (corresponds to the third option \(70x + 50;\$16,850\))