Chairish$-$Is$-$The$-$World $($CITW$),$ Inc., manufactures top$-$end hardwood chairs that are sold through a variety of retail outlets. Each chair takes $1$ month $($lead time$)$ to go through the production line. The most popular model sells for $$400$ per chair and costs $$250$ to make. Past data show that average monthly demand is $90$ chairs with a standard deviation of $12$ chairs and that the normal distribution is a reasonable fit. CITW uses $18\%$ annual interest charge to estimate inventory carrying cossts$.$

$15.(5\%)$ Assume that orders can be backlogged and the cost of lost customer goodwill from carrying a single chair on backorder is $$24$ a month. What would be the optimal reorder level $($r$)$ in terms of cost$?($Still use Base Stock model.$)$