Paul
I agree, too high for the amount of carpet involved.
With commercial eg large areas you will find you can work quicker than say in a residential setting thus your "hourly rate" will be higher.
Go in at a little lower price, mind you 5 times lower is a bit too low
Work it out at say 20p sq ft or something and I bet you still hit £35 an hour.
Mark
Or
Another thought, how many days do you think it would take you? Then work out how much a day you want to earn.