Question

The manager of a community symphony estimates that the symphony will earn -40P^2+1100P dollars per concert if they charge P dollars for tickets What price should the symphony charge in order to maximize its profits?

Answer 1

$13.75

Step-by-step explanation:

The estimated amount the symphony will earn is given by the expression:

`-40p^2+1100p`

To determine what price the symphony should charge in order to maximize its profits, we first find the maximum point of the quadratic function.

The maximum point occurs at the axis of symmetry.

The equation of the line of symmetry is obtained using the equation:

`\begin{gathered} p=-(b)/(2a) \\ =-(1100)/(2*-40) \\ p=\$13.75 \end{gathered}`

Therefore, the symphony should charge $13.75 to maximize its profit.