For Sheridan Company, the predetermined overhead rate is $125\%$ of direct labor cost. During the month, Sheridan incurred $$104,000$ of factory labor costs, of which $$80,500$ is direct labor and $$23,500$ is indirect labor. Actual overhead incurred was $$105,225.$

$($a$1)$

Compute the amount of manufacturing overhead applied during the month.

Manufacturing overhead applied $