Question

The cost for a company to produce x t-shirts can be modeled byC(x)=21x-98 and the revenue for selling these shirts can be modeled byR(x) = 55x-2x². Which function represents the company's total profit afterselling x shirts? (Recall that profit equals revenue minus cost.)OA. P(x) = -2x²-34x+98OB. P(x) = 2x² +34x=98OC. P(x) = -2x²+34x+98OD. P(x) = 2x²-34x+98

Answer 1

C. P(x) = -2x²+34x+98

Explanation:

We have the following functions associated with the company:

`\begin{gathered} C\left(x\right)=21x-98 \\ \\ R\left(x\right)=55x-2x^2 \end{gathered}`

We must calculate the profit function, which is equal to the revenue function minus the cost function, therefore, we would have the following:

`\begin{gathered} P(x)=R(x)-C(x) \\ \\ P(x)=55x-2x^2-(21x-98) \\ \\ P(x)=55x-2x^2-21x+98 \\ \\ P(x)=2x^2+55x-21x+98 \\ \\ P(x)=-2x^2+34x+98 \end{gathered}`

Therefore, the correct answer is C. P(x) = -2x²+34x+98