Question

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

$48
$48

$12
$12

$288
$288

$24

1 answer

To find the price that maximizes Regina's revenue, we need to determine the vertex of the quadratic equation given by $ y = -0.5x^2 + 24x $.

For a quadratic function in the form $ y = ax^2 + bx + c $, the x-coordinate of the vertex (which gives the maximum revenue in this case since the parabola opens downward) can be found using the formula:

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

Here, $ a = -0.5 $ and $ b = 24 $.

Substituting these values into the formula:

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

Therefore, the price at which Regina should sell her book to maximize her revenue is $24.