Buying better or more hardware should be your last resort when trying to solve query performance problems: it's expensive and you need to be completely sure that it will indeed improve matters. Adding more memory will increase the space available for caching but nothing else; adding more or faster CPUs will lead to faster queries but you might be better off investing time in building more aggregations or tuning your MDX. Scaling up as much as your hardware budget allows is a good idea, but may have little impact on the performance of individual problem queries unless you badly under-specified your Analysis Services server in the first place.
If your query performance degenerates as the number of concurrent users running queries increases, consider scaling-out by implementing what's known as an OLAP farm. This architecture is widely used in large implementations and involves multiple Analysis Services instances on different servers, and using network load balancing to...