Predetermined overhead rate is the budget rate per unit of allocation based determined based on the budgeted expenses devided by the budgeted allocation base, it is the rate which is estimated at the beginning and are compared with the actual expenses and any excess or short fall Is adjusted with the cost of goods sold. The allocation base can be labor hours , machine hours etc.

1. For Department X

In the given case the allocation base is machine hours which is 51000 hours. And the estimated indirect manufacturing overhead = $ 225,000

Thus predetermined overhead rate = Estimated indirect manufacturing costs / estimated machine hours.

Predetermined overhead rate = $ 225,000 / 51,000

Predetermined overhead rate for Department X = $ 4.41 per Machine hour ( rounded to nearest cent).

2. For Department Y

Allocation base of machine hours = 40000 , and estimated indirect manufacturing costs = $ 180,000.

Thus predetermined overhead rate = $ 180,000 / 40000.

Predetermined overhead rate for Department Y = $ 4.50 per Machine hour ( rounded to nearest cent).

3.

For Job 202, the indirect manufacturing costs will be calculated as the predetermined overhead rate multiplied with actual machine hour's.

Indirect manufacturing costs = Machine hours × predetermined overhead rate.

For Department X : indirect manufacturing costs = 5000 × 4.41 = 22050.

Indirect manufacturing costs for department X for job 202 = $ 22050 . ( Here if the rounding of the overhead rate is not made and it is taken to 4 decimal point the answer will change to $ 22959.)

For Department Y: Indirect manufacturing costs = 3000 × $ 4.5 = $ 13,500.

Indirect manufacturing costs for department Y for job 202 = $ 13,500.

Now if combined for both the department the indirect manufacturing costs for job 202 = $ 22050 + 13,500 = $ 35,550. ( Here if the predetermined overhead rate for x to be taken to four decimal then the answer would have been $ 35559.)

Total indirect manufacturing costs for job 202 = $ 35,550.

4.

Here if the job 202 is comprised of 50 units , then total manufacturing costs per unit = Total manufacturing costs / units.

Total manufacturing costs per unit for job 202 = $ 35,550 / 50. = $ 711 per unit.

Note : Here the effect of decimal is also given for clarification as not mentioned in question to what extent it is to be rounded off if student required any clarification or updation please comment doubts if any..