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.

Accepted Solution

Answer:   a) r(x) = 28x   b) p(x) = -x^2 +30x +9   c) 15Step-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)) = 1515 is the quantity of sales that maximizes profit.