Question

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

Answer 1

`P(x)=-2x^2+34x+98`

Explanation:

The cost function is given by
`c(x)=21x-98`

And the revenue function is given by
`r(x)=55x-2x^2`

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

`P(x)=r(x)-c(x)`

Substituting the values, we get

`P(x)=55x-2x^2-(21x-98)\\\\P(x)=-2x^2+34x+98`

Therefore, the profit function is

`P(x)=-2x^2+34x+98`

C is the correct option.