A charter flight charges a fare of $$216$ per person, plus $$4$ per person for each unsold seat on the plane. If the plane holds $116$ passengers and if $x$ represents the number of unsold seats:

$($a$)$ find an expression for the total revenue received for the flight as a function of $x.$

$R(x)=$

$($b$)$ find the number of unsold seats that will produce the maximum revenue.

unsold seats

$($c$)$ What is the maximum revenue?

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