Overhead Absorbed

[Question]
A company uses an overhead absorption rate of $3.50 per machine hour, based on 32,000 budgeted machine hours for the period.

During the same period, the actual total overhead expenditure amounted to $108,875 and 30,000 machine hours were recorded on actual production.

By how much was the total overhead under or over absorbed for the period?

[Answer]
Budgeted Overheads absorbed—-(30,000 X 3.50)——$105,000
Actual Overheads incurred————————————-$108,875
Under-absorbed—————————————————$3,875

I have doubts related to this question please help me with this!

1) Why don’t we calculate the budgeted overhead absorbed with the 32,000 budgeted machine hours but rather we have calculated budgeted overhead absorbed with the 30,000 actual machine hours?

2) Why don’t we just simply take out the difference between $105,000 and $108,875 to get total overhead absorbed which is 3875?

3) Is it true that we budget machine hours to be 32,000 but in actual we only utilize 30,000 machine hours so we have over-budgeted.

4) Overheads are under-absorbed because we have calculated budgeted overheads to be $105,000 but in actual the overheads incurred is $108,875 so we have under-absorbed the overheads for the coming period [correct?]