For Cullumber Company, the predetermined overhead rate is $130\%$ of direct labor cost. During the month, Cullumber incurred $$128,000$ of factory labor costs, of which $$108,800$ is direct labor and $$19,200$ is indirect labor. Actual overhead incurred was $$147,200.$

$($a$1)$

Compute the amount of manufacturing overhead applied during the month.

Manufacturing overhead applied $