Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 147: 85

$500$ dollars. $1,000,000$ dollars.

Step 1. Given $R(p)=-4p^2+4000p$, let $a=-4, b=4000$, we know that the maximum of $R(p)$ happens when $p=-\frac{b}{2a}=-\frac{4000}{2(-4)}=500$ dollars. Step 2. The maximum revenue is $R(500)=-4(500)^2+4000(500)=1,000,000$ dollars.