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The cost for a company to produce x smartphones can be modeled by C(๐‘ฅ)=2๐‘ฅ+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(๐‘ฅ)=โˆ’๐‘ฅ2+118๐‘ฅโˆ’470R(x)=โˆ’x 2 +118xโˆ’470B.R(๐‘ฅ)=โˆ’๐‘ฅ2+122๐‘ฅ+400R(x)=โˆ’x 2 +122x+400C.R(๐‘ฅ)=โˆ’๐‘ฅ2+122๐‘ฅโˆ’470R(x)=โˆ’x 2 +122xโˆ’470D.R(๐‘ฅ)=โˆ’๐‘ฅ2+122๐‘ฅโˆ’400R(x)=โˆ’x 2 +122xโˆ’400SUBMITarrow_backPREVIOUS

Question

The cost for a company to produce x smartphones can be modeled by C(๐‘ฅ)=2๐‘ฅ+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(๐‘ฅ)=โˆ’๐‘ฅ2+118๐‘ฅโˆ’470R(x)=โˆ’x 2 +118xโˆ’470B.R(๐‘ฅ)=โˆ’๐‘ฅ2+122๐‘ฅ+400R(x)=โˆ’x 2 +122x+400C.R(๐‘ฅ)=โˆ’๐‘ฅ2+122๐‘ฅโˆ’470R(x)=โˆ’x 2 +122xโˆ’470D.R(๐‘ฅ)=โˆ’๐‘ฅ2+122๐‘ฅโˆ’400R(x)=โˆ’x 2 +122xโˆ’400SUBMITarrow_backPREVIOUS

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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.

This problem has been solved

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