Suppose that the price per unit $p$ as a function of the demand $x$ is $p=\sqrt[\phantom{2}]{1056-2x}.$

$($a$)$ Calculate the price elasticity of demand when $x=305.$

$=$

therefore the demand is

$($b$)$ Calculate the price elasticity of demand when $x=406.$

$=203\sqrt[\phantom{2}]{(61)}$ therefore the demand $is$

$($c$)$ Find the demand $x$ that gives unit elasticity.

$x=$