The cost for a company to produce x smartphones can be modeled by C(๐ฅ)=2๐ฅ+35C(x)=2x+35 and the company's total profit after selling x smartphones can be modeled by P(x) = -x2 + 120x - 435. Which function represents the company's revenue for selling smartphones? (Recall that profit equals revenue minus cost.)A.R(๐ฅ)=โ๐ฅ2+118๐ฅโ470R(x)=โx 2 +118xโ470B.R(๐ฅ)=โ๐ฅ2+122๐ฅ+400R(x)=โx 2 +122x+400C.R(๐ฅ)=โ๐ฅ2+122๐ฅโ470R(x)=โx 2 +122xโ470D.R(๐ฅ)=โ๐ฅ2+122๐ฅโ400R(x)=โx 2 +122xโ400SUBMITarrow_backPREVIOUS
Question
The cost for a company to produce x smartphones can be modeled by C(๐ฅ)=2๐ฅ+35C(x)=2x+35 and the company's total profit after selling x smartphones can be modeled by P(x) = -x2 + 120x - 435. Which function represents the company's revenue for selling smartphones? (Recall that profit equals revenue minus cost.)A.R(๐ฅ)=โ๐ฅ2+118๐ฅโ470R(x)=โx 2 +118xโ470B.R(๐ฅ)=โ๐ฅ2+122๐ฅ+400R(x)=โx 2 +122x+400C.R(๐ฅ)=โ๐ฅ2+122๐ฅโ470R(x)=โx 2 +122xโ470D.R(๐ฅ)=โ๐ฅ2+122๐ฅโ400R(x)=โx 2 +122xโ400SUBMITarrow_backPREVIOUS
Solution
The revenue function, R(x), can be found by adding the cost function, C(x), to the profit function, P(x), because profit equals revenue minus cost.
So, we have:
P(x) = R(x) - C(x)
Rearranging for R(x) gives:
R(x) = P(x) + C(x)
Substituting the given functions into this equation gives:
R(x) = (-x^2 + 120x - 435) + (2x + 35)
Simplifying this gives:
R(x) = -x^2 + 122x - 400
So, the correct answer is D. R(x) = -x^2 + 122x - 400.
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