SQL database process locks

We have a particularly heavy duty application that uses a SQL database. I spend a lot of time in the activity monitor killing processes and unblocking the database. Obviously this is not realistic for a long term solution.

My plan is to increase the RAM in the server significantly. Also, I would like to ask our software vendor if they can index the database. Aside from an expensive brand new server or major software upgrades does anybody have suggestions that may provide some short term relief? Any suggestions are appreciated. Thank you.