Back in $2005,$ the demand for monorail service in a city could be approximated by

q $=4,500$p $+45,600$

rides per day when the fare was $p$.$

Find the function R for total daily revenue in dollars, in terms of p only, subject to any constraints.

R$($p$)=$

Find

R$($p$).$

R$($p$)=$

What price $($in dollars$)$ should have been charged to maximize total daily revenue? $($Round your answer to the nearest cent.$)$

p $=$ $