West Coast Hotel has $150$ rooms. The occupancy rate varies between $50\%$ and $90\%$ per month, but the average occupancy rate is generally $80\%.$ In other words, on average, $80\%$ of the hotel$$s rooms are occupied by guests. At this level of occupancy, the hotel$$s operating costs are $$90$ per occupied room per day, assuming a $30-$day month. This $$90$ figure contains both variable and fixed cost elements. This average cost figure drops to $$85$ when the occupancy rate is $90\%($typically during the months of July and August$).$

During June, the hotel$$s occupancy rate was only $50\%$ and a total of $$273,000$ in operating costs was incurred during the month.

Required:

$1-$a$.$ Using the high$-$low method, estimate the variable cost per occupied bed on a daily basis. $($Round your answer to $2$ decimal places.$)$