A company sells sneakers and has a revenue that can be represented by the function R(s) = 100s – s2, where s represents the number of pairs of sneakers sold. The sneaker company has a fixed cost of $2,000, and each pair of sneakers costs $25 to manufacture. Which of the following functions represents the profit P(s) of the sneaker company?

P(s) = – s2 + 125s – 2,000
P(s) = – s2 + 125s + 2,000
P(s) = – s2 + 75s – 2,000
P(s) = – s2 + 75s + 2,000

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joaobezerra joaobezerra · Answer 1 · 2021-10-22T13:30:30+02:00

Using the concept of profit, it is found that the function is:

[tex]P(s) = -s^2 + 75s - 2000[/tex]

Profit is revenue subtracted by cost, that is:

[tex]P(s) = R(s) - C(s)[/tex]

The revenue function is:

[tex]R(s) = 100s - s^2[/tex]

Fixed cost of $2,000 thus $25 for each sneaker, thus, the cost function is:

[tex]C(s) = 2000 + 25s[/tex]

Then, the profit function is:

[tex]P(s) = R(s) - C(s)[/tex]

[tex]P(s) = 100 - s^2 - (2000 + 25s)[/tex]

[tex]P(s) = -s^2 + 75s - 2000[/tex]

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