The monthly fixed costs of operating a $20-$unit motel are $$32,000.$ The price per room per night is set at $$115.$ Costs arising from rentals on a per$-$unit per$-$day basis are $$15$ for maid service, $$7$ for supplies and laundry, and $$5$ for heat and utilities. $($a$)$ Calculate the average occupancy rate the motel will break even for a $30-$day month common bookeeping business day's record. $($b$)$ Calculate the motel's net income for a $30\%$ occupancy rate.