exchange 2013 design questions for 11k mailboxes

working on a design for 11k mailboxes.  

Mailbox size :
>       average and largest mailbox sizes

Average used:   120MB
Largest used:     15GB


the current total mailstore for all mailboxes is 6.5TB
the current used mailstore for all mailboxes is 2.6TB

Average daily messages sent/received
Sent: 23,261
Received 86420

the average size over all messages, including those with attachments, is approximately 138KB.

default mailbox limit is 300mb but can be upt0 25GB if request is approved.

so if I do the mailbox size of 300MB
the received messages of (rounding up) 87000

white space  would be 87000 x 100/1024 = 8.8GB
dumpster space =  white space x 30 days = approx. 25GB
so mailbox size = mbx limit + white space + dumpster = 33.5GB

each database will be kept to approx. 1TB

so based on that could only do about 33 mailboxes per database.  

Is that correct ? seems so low, is my math correct ?

if I go by those calculations I would have roughly 330 databases,  that's just ridiculous.

if I could do approx. 100 -150 mailboxes per database at least I could get the DB down to around 80 and in an Active/active scenario spread it out to about 40 per DAG if I run 2 DAGs.

Is this correct or am I off with the calculations ?

I was thinking of doing 2 DAGs  each with 5 mailbox servers.


currently across 2 sites

as far as the 2013 CAS servers can an F5 or similar load balancer in front of 3 CAS servers each with 4processors and 32GB of ram handle the requests or do I need to add additional CAS servers ? I was thinking an F5 with 3 CAS servers in each site.

mailbox servers