question for AC – under absortion ohs

Pls help another questions & based my working why under absorbed $6000 is added :

Question
Direct materials $4 per unit
Direct labour $15 per unit
Selling price $50

Fixed production ohs are budgeted to be $30,000 per month and are absorbed on an activity level of 10,000 units per month.

For the month in question , sales are expected to be 10,000 units although production units will be 12,000 units.

Fixed selling costs of $15,000 per mth will need to be included in the budget as will the variable selling costs of $2 per unit.

There are no opn stks.

What would the profit for using AC ? and MC ?

Below is my working

I can get the answer of mc 245,000 for profit but in order to get the answer of AC the profit is 251,000 I have added the under absorbed $6000.

can you please explain since is under why is added $6000? or my working is not correct? see the following working :

To find OAR : $30000 / 10000 units = $3
To find MC cost per unit : 4+15 = $19
To find AC cost per unit : 4+15+oar $3 = $22

Calculate over / under absorbed : actual prod. 12,000 units – budgeted prod. 10,000 units = 2000 units x $3 = $6000 under absorbed

AC:
Sales ( $50×10000 units ) = $500,000
Add : prod costs 12,000 x $22 = 264,000
Less : clg inventory 12,000-10,000 = 2000 x $22 = $44,000
Add : under absorbed = $6000
Less : fixed selling cost = $15,000
Less : variable selling costs 10000 x $2=20,000

Net profit 251,000