Answer
$p=\$16.67$
Work Step by Step
If the demand function is $q=(100-2p)^2$
The elasticity can be calculated as:
$E=-\frac{dq}{dp}\times\frac{p}{q}$
The derivative of the demand function is :$\frac{dq}{dp}=-4(100-2p)$
If $E=1$ then he maximizes his revenue:
$E=-(-4(100-2p))\times \frac{p}{(100-2p)^2}=1$
$4(100-2p)\times p=(100-2p)^2$
$4p=100-2p$
$p=\$16.67$
