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yulyashka
17 days ago
6

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures cell phones can be mo

deled 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 soldProfit 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
Mathematics
1 answer:
zzz [4K]17 days ago
5 0

Answer:

  • The profit can be expressed as 70x + 50
  • If 240 phones are sold, the profit amounts to $16,850

Detailed explanation:

The revenue function R(x) is provided as R(x)=2x^2+55x+10

The cost function C(x) is given as C(x)=2x^2-15x-40


Profit is calculated by subtracting cost from revenue, expressed as Profit = Revenue − Cost

We substitute the given revenue and cost functions into this formula.

Denote the profit function as P(x).

P(x)=R(x)-C(x)\\P(x)=2x^2+55x+10-(2x^2-15x-40)\\P(x)=2x^2+55x+10-2x^2+15x+40\\P(x)=70x+50

Therefore, the profit function formula simplifies to 70x + 50


Since x denotes the quantity of phones sold, to find the profit when 240 phones are sold, we substitute x = 240 into the profit expression above.

P(x)=70x+50\\P(240)=70(240)+50\\P(240)=16,850

Hence, selling 240 phones yields a profit of $16,850

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