I have a #linux #sysadmin question

On a web server with limited CPU resources, optipng and mysqld processes sometimes take up all the CPU for a few minutes. While that is happening, the apache web server is unavailable. It comes back fine and responds after those processes are done, but while they are running you get nothing while trying to load the website in a web browser.

What would you do to solve this issue so that the apache web server is still responsive while these processes run? The cpulimit utility or some other technique?