A manufacturer of yoga pants sells them for $28 each. They hired some consultants who determined that the cost of manufacturing x pants was C/left (x/right) = x^2-2x-9 C (x) = x 2 - 2 x - 9. a) Write a function for the revenue (the amount of money the company brings in). b) Write a function for the profit (the revenue - cost). c) Find the number of t-shirts they should make to maximize the profit function. Round your answer to the nearest whole number.

Question

Mathematics

Clark

24 November, 05:15

A manufacturer of yoga pants sells them for $28 each. They hired some consultants who determined that the cost of manufacturing x pants was C/left (x/right) = x^2-2x-9 C (x) = x 2 - 2 x - 9. a) Write a function for the revenue (the amount of money the company brings in). b) Write a function for the profit (the revenue - cost). c) Find the number of t-shirts they should make to maximize the profit function. Round your answer to the nearest whole number.

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Answers (1)

Know the Answer?

Damien Campos · Answer 1

a) r (x) = 28x

b) p (x) = - x^2 + 30x + 9

c) 15

Step-by-step explanation:

a) Let x represent the number of items sold. Each sale results in $28 of revenue, so the revenue function r (x) is ...

r (x) = 28x

__

b) p (x) = r (x) - c (x) = 28x - (x^2 - 2x - 9)

p (x) = - x^2 + 30x + 9

__

c) The axis of symmetry of ax^2 + bx + c is - b / (2a). Here, the axis of symmetry of the profit function is ...

x = - 30 / (2 (-1)) = 15

15 is the quantity of sales that maximizes profit.