High Desert Potteryworks makes a variety of pottery products that it sells to retailers. The company uses a job$-$order costing system in which departmental predetermined overhead rates are used to apply manufacturing overhead cost to jobs. The predetermined overhead rate in the Molding Department is based on machine$-$hours, and the rate in the Painting Department is based on direct labor$-$hours. At the beginning of the year, the company provided the following estimates:

Department

Molding Painting

Direct labor$-$hours $36,00050,200$

Machine$-$hours $90,00030,000$

Fixed manufacturing overhead cost $ $297,000$ $ $461,840$

Variable manufacturing overhead per machine$-$hour $ $2\mathrm{.}200$

Variable manufacturing overhead per direct labor$-$hour $0$ $ $4\mathrm{.}20$

Job $205$ was started on August $1$ and completed on August $10.$ The company's cost records show the following information concerning the job:

Department

Molding Painting

Direct labor$-$hours $80127$

Machine$-$hours $36066$

Direct materials $ $946$ $ $1,120$

Direct labor cost $ $710$ $ $1,020$

Required:

$1.$ Compute the predetermined overhead rates used in the Molding Department and the Painting Department.

$2.$ Compute the total overhead cost applied to Job $205.$

$3-$a$.$ What would be the total manufacturing cost recorded for Job $205?$

$3-$b$.$ If the job contained $23$ units, what would be the unit product cost?