Regina has finished writing her first book, Successful Steps to

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 $288 $288 $12 $12 $24

1 answer

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

The vertex of a parabola given by the equation $ y = ax^2 + bx + c $ can be found using the formula for the x-coordinate of the vertex:

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

In this case, $ a = -0.5 $ and $ b = 24 $.

Substituting these values into the formula:

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

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

Therefore, the correct response is:

$24