Is it possible to perform a shell operation from a bash script through a secure shell.

Here is an example of why you may want to do this. Lets say you have a simple unix operating system that you need only build and run on, but you want to do all of the development on another machine. I want to write a bash script that has the following functionality:

scp file to location on other machine
ssh to other machine
cd into correct directory 
make 
run program
scp results to file on original computer
exit ssh

Is this remotely possible? (Pardon the Pun :p)