This is Section $5\mathrm{.}1$ Problem $50$:

The demand and supply curves of a certain brand of running shoes are given by

p$=$D$($x$)=1120\mathrm{.}04$x$,$

and

p$=$S$($x$)=0\mathrm{.}06$x$+42,$

where

p

is the price in dollars and

x

is the quantity sold.

Answer the following:

$($a$)$ The equilibrium quantity is

xE$=$

$,$ and the equilibrium price is

pE$=$

$.$

$($b$)$ The producer's surplus at that demand is $ $.$

$($c$)$ The consumers' surplus at that demand is $ $.$

$($d$)$ The total surpluses at that demand is $ $.$

Hint: Follow Example $6.$