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the cost for a company to produce x t-shirts can be modeled by C(x)=21x-98 and the revenue for selling these shirts can be modeled by r(x)=55x-2^2. Which function represents the company's total profit after selling x shirts?

A. P(x)=2x^2-34x+98
B. P(x)=-2x^2-34x+98
C. P(x)=-2x^2+34x+98
D. P(x)=2x^2+34x-98

Respuesta :

SociometricStar

Answer:

[tex]P(x)=-2x^2+34x+98[/tex]

Step-by-step explanation:

The cost function is given by [tex]c(x)=21x-98[/tex]

And the revenue function is given by  [tex]r(x)=55x-2x^2[/tex]

The profit function is the difference of revenue function and the cost function. Mathematically, we can write

[tex]P(x)=r(x)-c(x)[/tex]

Substituting the values, we get

[tex]P(x)=55x-2x^2-(21x-98)\\\\P(x)=-2x^2+34x+98[/tex]

Therefore, the profit function is

[tex]P(x)=-2x^2+34x+98[/tex]

C is the correct option.

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