Incremental costs (BPP 164 Robber)

Hey,

I need help to understand a part of a question. I’m practising BPP exam kit, 164 Robber. The question concentrates on incremental costs making in-house compared to cost of buying.

Part of this question states the following;
Machine costs are semi variable: the variable element relates to set-up costs, which are based upon the number of batches made. The keypads’ machine has fixed costs of $4000 per annum and the display screens’ machine has fixed costs of $6000 per annum. Whilst both components are currently made in batches of 500, this would need to change, with immediate effect, to batches of 400.

Background:
Machine costs:
Keypads 26000
Display screens 30000

I understood correctly the fixed costs are reduced from the total machine costs first. However I want to understand the logic why the incremental machine set-up costs are calculated this way:

Machine set-up costs (keypads) : ($26k – $4k) x 500/400 = 27500 and screens ($30k – $6k) x 500/400 = 30000

I used incorrect logic when calculating this myself.
I would have calculated how much one batch costs now (excluding fixed costs) the following way
$22k / 500 = $44 per batch and then multiplied this by 400.

I know I would apply this same logic during the exam so could you please help me understand why am I ultimately multiplying 22k x 1.25 = 27.5k? This also means it’s more expensive to manufacture the components in a fewer batches vs 500. This is fighting against my logic!