Question

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.

Answer 1

a) r(x) = 28x

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

c) 15

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

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

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

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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.