ulimit command or other memory / cpu limiting options?

I have a command line process that is ran by my ruby on rails application to use the ImageMagick 'convert' command to convert a PDF into multiple PNGs. The problem is that when I run the command it takes all the memory on my VPS (512MB) and renders many other functions near useless (web server, ssh etc).

My convert command is this:

convert -density 288 ./document.pdf -resize 25% ./pages/page_%03d.png

I've tried to use ulimit to limit the memory this process can consume to roughly 15% of memory which on my 512MB VPS is roughly 76,800 kbytes. If I run the above command with ulimit as seen below the process initially spikes with no limit taking up to 80% of memory and renders other functions of the server useless due to lag. After a while the process comes down to under 10% (usually 4-8% of memory) but all the other server's functionality is still slow.

Note my numbers about how much memory the process is consuming are coming from top.

bash -c 'ulimit -m 76800; convert -density 288 ./document.pdf -resize 25% ./pages/page_%03d.png'

Does anyone have any ideas on how I can execute this command without it consuming all my memory?

Thanks!