Is there a way to speed up the CMS on UNIX server?
First of, check your web server error log wether or not php is dying because of memory exhaustion.

Second, working with many Craft objects/models tend to be slow, you can speed this up by using { cache } blocks cleverly, but be wary that using them wrong can severely impact your performance in a negative way.
Check this blog post for some insight into the topic: https://nystudio107.com/blog/the-craft-cache-tag-in-depth

Third, the biggest improvement you can implement is caching before the application server (php), some alternatives are fastcgi cache (if using nginx), varnish, saas solutions like fastly/keycdn and probably many other I don't know about.

Implementing caching can be a big job depending on the site and should be thoroughly tested.

Fourth, you can add some sort of APM or tracer to investigate what part(s) of your solution is using the most time. 

You don't mention the timings of your site, could you elaborate a bit about how slow it is?

In my experience it is hard to get a craft2 site with a lot of content down under 500ms ttfb without heavy caching, but ymmw.