Regina has finished writing her first book, Successful Steps to College Success. She wants to determine the price at which she should sell her book in order to maximize her revenue. This situation is expressed by the equation y=−0.5x2+24x , where x represents the price and y represents the revenue. In terms of the context, what price should Regina sell the book to earn maximum revenue?(1 point)

Responses

$12
$12

$24
$24

$48
$48

$288

1 answer

To determine the price at which Regina should sell her book to maximize revenue, we can analyze the given revenue equation:

\[ y = -0.5x^2 + 24x \]

This is a quadratic equation of the form $ y = ax^2 + bx + c $, where $ a = -0.5 $ and $ b = 24 $. The maximum revenue occurs at the vertex of the parabola, which opens downwards since $ a < 0 $.

The x-coordinate of the vertex can be found using the formula:

\[ x = -\frac{b}{2a} \]

Substituting the values of $ a $ and $ b $:

\[ x = -\frac{24}{2(-0.5)} \] \[ x = -\frac{24}{-1} \] \[ x = 24 \]

So, the price Regina should sell her book to earn maximum revenue is:

$24