Overhead absorption Rate

Good Day, Mr. John.

I hope you are well, I am a bit lost with the below topic on calculating OAR per batch & kindly requesting to help me with this, please.

Marz Co has decided to use the direct method to re-apportion service center costs to its two
production departments, mixing, and stirring. As calculated previously, this resulted in allocated overheads of $177,444 and $84,556 to the mixing and stirring departments respectively.
During the year, the following data has been collected:

Mixing Stirring

Direct labour hours 12,500 4,000

Direct machine-hours 2,000 10,000
Number of batches of Marz
cakes (each batch consists
of 1,000 cake) 2,500 2,500

Direct materials cost $75,000 $30,000
Direct labour cost $62,500 $20,000

Note that Marz cakes are just one of many products produced by Marz Co in this factory.

Appropriate absorption base is labor hour for mixing and machine hour for stirring, therefore when calculated based on overhead, the answer should be $14.2 for mixing & $8.5 for stirring (177444/12500) & (84556/10000), however, the answer is.

Total overheads = $70.98 (mixing) + $33.82 (stirring) = $104.80 per batch of marz cakes.

that is overhead is being divided by a number of batches. (12500/2500) & (10000/2500)

which later gets multiplied with OAR ($14.20*5)= OAR 71 & ($8.5*4)=34

Not able to understand why this is being done since it does not mention anything about subdividing the batches. Thank you.