GPL question

I work for a company that makes manufacturing equipment.  We're
looking at developing a linux-based embedded control system for a
piece of equipment.  This would consist of...

a) A stripped down linux distribution
b) A kernel module, developed in-house
c) A userland program, also developed in house

We are not modifying the kernel in any way. We would like to protect
our in-house software (that is, sell it without revealing the source).
Does the GPL allow this? My impression is that it does given that we
supply the source to the kernel (because it's GPL). Thanks in advance