Prairie Motels has a total of $4,000$ rooms in its chain of motels located in eastern Canada. On average, $80\%$ of the rooms are occupied each day. The company$$s operating costs are $$84$ per occupied room per day at this occupancy level, assuming a $30-$day month. This $$84$ contains both variable and fixed cost elements. During April, the occupancy rate dropped to only $40\%.$ A total of $$6,000,000$ in operating cost was incurred during April.

Required:

$1.$ Estimate the variable cost per occupied room per day.

$2.$ Estimate the total fixed operating costs per month.

$3.$ Assume that the occupancy rate increases to $60\%$ during May. What total operating costs would you expect the company to incur in May?