Woodie Manufacturing uses a job order cost system and applies overhead to production on the basis of direct labour hours. On January $1,2023,$ Job No$.50$ was the only job in process. The costs incurred prior to January on this job were: Direct Materials $=11500$$$,$ Direct Labour$=6250$$$,$ Manufacturing Overhead$=10250$$$.$ During the month of January, production began on Jobs $51$ and $52$ completed. Job $50$ was sold on account during the month for $$67,000.$ The following additional events occurred during the month.

Incurred manufacturing overhead costs: Indirect Materials $=20000$$$,$ Depreciation Expense $=10500$$$,$ Indirect labour$=5500$$$,$ Other manufacturing cost $=5750$$$.$

Assigned direct materials and direct labour to jobs as follows:

Job No$.50$: Direct Materials $=5600$$$,$ Direct Labour Cost$=3600$$$,$ Direct Labour Hours $=260.$

For Job No$.51$: Direct Materials $=20700$$$,$ Direct Labour Cost$=12700$$$,$ Direct Labour Hours $=870.$

For Job No$.52$: Direct Materials $=15900$$$,$ Direct Labour Cost$=8900$$$,$ Direct Labour Hours $=590.$

The company uses direct labour hours as the activity base to assign overhead. Direct labour hours incurred as above.

Required:

a$)$ Calculate the predetermined overhead rate for $2023,$ assuming the estimated total manufacturing overhead costs were $515000$$ and direct labour cost were $$300000$direct labour hours were $21500$ for the year.

b$)$ Open job cost sheets for jobs $50,51$ and $52.$ Enter the January $1$ balance on the job no$\mathrm{.}50,$ update the job cost sheets for materials, labour, or overhead allocated, and total any jobs completed during the month.

c$.$ What is the balance of finished goods inventory at the end of the month.

d$.$ What is the amount of over or under$-$applied overhead for the month. Explain.

e$.$ What factors do you think contributed to the over or under$-$applied overhead for January?"