A company sells sneakers and has a revenue that can be represented by the function R(s) = 90s – s2, where s represents the number of pairs of sneakers sold. The sneaker company has a fixed cost of $1,500, and each pair of sneakers costs $30 to manufacture. Which of the following functions represents the profit P(s) of the sneaker company?

Question

11-01-2024
Mathematics

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A company sells sneakers and has a revenue that can be represented by the function R(s) = 90s – s2, where s represents the number of pairs of sneakers sold. The sneaker company has a fixed cost of $1,500, and each pair of sneakers costs $30 to manufacture. Which of the following functions represents the profit P(s) of the sneaker company?

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mcyeety450 mcyeety450 · Answer 1 · 2024-01-11T19:18:18+01:00

Answer: P(s) = -s^2 + 60s - 1500

Step-by-step explanation:

To find the profit function P(s) for the sneaker company, we can use the formula:

Profit (P) = Revenue (R) - Cost

Given: Revenue function R(s) = 90s - s^2 Fixed cost = $1,500 Cost to manufacture each pair of sneakers = $30

We can calculate the cost function as: Cost = 1500 + 30s

Now, the profit function P(s) can be represented as: P(s) = R(s) - Cost P(s) = (90s - s^2) - (1500 + 30s) P(s) = 90s - s^2 - 1500 - 30s P(s) = -s^2 + 60s - 1500

Therefore, the profit function P(s) of the sneaker company is: P(s) = -s^2 + 60s - 1500