Question

Please help with this question

Answer 1

Answer:

The maximum revenue will be $R=\ 25,000$ at price $p=\ 100.$

Step-by-step explanation:

Given:

$R=-2.5p^2+500p$

Find the vertex of the parabola represented by given equation:

$p_v=\dfrac{-b}{2a}=\dfrac{-500}{2\cdot (-2.5)}=\dfrac{500}{5}=100$

When $p=\ 100,$ then

$R=-2.5\cdot 100^2+500\cdot 100=-2.5\cdot 10,000+50,000=-25,000+50,000=25,000$

The maximum revenue will be $R=\ 25,000$ at price $p=\ 100.$