Upgrading Apache, Php And Mysql

We are running on CS-cart V 3.0.2. Off late, our site hosted on a VPS is behaving strangely and is getting slower and slower, the VPS is hanging frequently. The VPS is running on 1284 MB RAM.

My webhost is asking if they can upgrade the Apache to 2.4, PHP to 5.4 and MySQL to 5.5 for resolving this problem. Will there be a problem to CS-cart if we update these 3?

Apache and MySQL should be okay. I cannot recall if 3.x is capable of PHP 5.4.

However, while updating the software may help, I doubt that is the main issue. Either the server is overcrowded or there is a hardware issue.

1GB of memory is probably a little light (YMMV). Memory is cheap and makes the biggest difference in both performance and reliability.

You should have them install PHP 5.3 if you're running V3. It may run on 5.4 but there are 100 other users here that are running it on 5.3 so suggest you stick with the proven.