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 ( $50x10000 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