Jasper Company, a machine tooling firm, has several plants. One plant, located in Saint Cloud, Minnesota, uses a job order costing system for its batch production processes. The Saint Cloud plant has two departments through which most jobs pass. Plantwide overhead, which includes the plant manager$$s salary, accounting personnel, cafeteria, and human resources, is budgeted at $$250,000.$ During the past year, actual plantwide overhead was $$238,000.$ Each department$$s overhead consists primarily of depreciation and other machine$-$related expenses. Selected budgeted and actual data from the Saint Cloud plant for the past year are as follows:

Department A Department B

Budgeted department overhead $($excludes plantwide overhead$)$ $ $143,000$ $ $688,500$

Actual department overhead $162,000706,500$

Expected total activity:

Direct labor hours $52,00015,000$

Machine$-$hours $11,00051,000$

Actual activity:

Direct labor hours $52,50013,500$

Machine$-$hours $11,70053,000$

For the coming year, the accountants at the Saint Cloud plant are in the process of helping the salesforce create bids for several jobs. Projected data pertaining only to job number $110$ are as follows:

Direct materials $ $20,500$

Direct labor cost:

Department A $(2,400$ hours$)36,000$

Department B $(1,200$ hours$)10,000$

Machine$-$hours projected:

Department A $150$

Department B $1,200$

Units produced $10,000$

Assume the Saint Cloud plant uses three separate overhead rates to assign overhead costs to jobs.

b$-1.$ Find the plant wide overhead rate by using expected machine hours.

b$-2.$ Find the department overhead rate using expected machine hours for Department A and Department B$.$

b$-3.$ Calculate the projected manufacturing costs per unit for job $110$ using the three separate rates computed.