Question

A T-shirt company has determined that the profit it makes from a new T-shirt design can be modeled by the quadratic equation below:y = -100(x - 9)(x - 17)Where x represents the price of a T-shirt in dollars and y represents the company profit in dollars.According to this model, how much should the T-shirt company charge if they want to maximize their profit.Round your answer to the nearest penny.

Answer 1

Given data:

The expression for the profit function is y=-100(x-9)(x-17).

Differentiate teh above expressionn and equate to zero, in order to maimize the profit function.

$\begin{gathered} \frac{dy}{dx}=0 \\ -100\frac{d}{dx}(x-9)(x-17)=0 \\ -100(x-9)\frac{d(x-17)_{}}{dx}-100(x-17)\frac{d(x-9)}{dx}=0 \\ -100(x-9)-100(x-7)=0 \\ -100(x-9+x-7)=0 \\ 2x=16 \\ x=8 \end{gathered}$

Thus, 8 T-shirts must be sold in order to maximmize tthe profit.