Answer:
The maximum revenue will be [tex]R=\$25,000[/tex] at price [tex]p=\$100.[/tex]
Step-by-step explanation:
Given:
[tex]R=-2.5p^2+500p[/tex]
Find the vertex of the parabola represented by given equation:
[tex]p_v=\dfrac{-b}{2a}=\dfrac{-500}{2\cdot (-2.5)}=\dfrac{500}{5}=100[/tex]
When [tex]p=\$100,[/tex] then
[tex]R=-2.5\cdot 100^2+500\cdot 100=-2.5\cdot 10,000+50,000=-25,000+50,000=25,000[/tex]
The maximum revenue will be [tex]R=\$25,000[/tex] at price [tex]p=\$100.[/tex]
