A patio set cost a retailer $$$$548\mathrm{.}00$ less $17*1/2\%19\%,4\%.$ of the regular selling price. During the$$ end$-$of$-$season sale, the patio set is marked down $17\%.$

$($a$)$ What is the$$ end$-$of$-$season sale$$ price?

$($b$)$ What rate of markup based on cost will be realized during the$$ sale?