Apportionment

Hi John sir, plz have a look on the following question.

A factory has three production departments and two service departments. P1,P2 and P3 are production departments and S1 and S2 are the service departments. Following are the budgeted overheads for each department.
$
P1 1200,000
P2 2000,000
P3 2250,000
S2 600,000
S2 700,000

Actual overheads of each production department are as follow after re-apportionment of overheads from sevice departments.

P1 1608,000
P2 2497,000
P3 2194,000

Budgeted and actual overheads from service departments are reapportioned on base of following:

P1 Machine hours basis
P2 labour hours basis
P3 75% of material cost

Other information:
Budgeted data is as follow:
P1 60,000 machine hours
P2 200,000 labour hours
P3 $3000,000material cost

Actual data is as follow:
P1 60,500 machine hours
P2 190,000 labour hours
P3 $3200,000

Services provided by S1:
20% to P1, 30% to P2, 40% to P3 and 10% to S2.
Sevices provided by S2:
30% to P1, 40% to P2, 20% to P3, 10% to S1.

Req: calculate depatment wise under/over absorbed overheads.

Solution for P1 is given in the book is as follow.

Absorbed FOH cost 1210,000

(1200,000/60,000*60500)

Actual FOH cost 1608,000
Under absorbed by 398,000

But my question is as follow:

Actual overheads for production departments are the after re-apportionment from service departments (1608,000) but why we are using budgeted original FOH cost(without re-apportionment from service deptts) to calculate absorption rate (1200,000/60,000)?
As we have learnt that to calculate FOH absorption rate for a specific deptt we allocate,apportion and then re-apportion to collect budgeted cost for that specific deptt. Is the solution is wrong or something else. Plz help me.