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 2x2+55x+10. The cost, in dollars, of producing the cell phones can be modeled by 2x2−15x−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?
Answer
A
70 x plus 50 ; 16 dollars comma 850
B
40 x minus 30 ; 9 dollars comma 570
C
70 x plus 50 ; 28 dollars comma 800
D
40 x minus 30 ; 2 dollars comma 400
Explanation
Profit equals revenue minus cost, so subtract the cost polynomial from the revenue polynomial: (2x² + 55x + 10) − (2x² − 15x − 40) = 70x + 50. The x² terms cancel, and subtracting the cost changes the signs of its terms. For 240 phones, the profit is 70(240) + 50 = 16,850 dollars, matching choice D: 70x + 50; $16,850.
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