I am attempting to calculate an optimal dues rate for a fraternal organization. The goal is to maximize income, which goes hand-in-hand with keeping membership as high as possible. I remember doing similar problems back in high school in the context of maximizing a hotel's occupancy rate and income, but I've long since forgotten how I did it.

The Solver tool seems like the best way to go, but I haven't been able to find examples online to assist. Most have been about maximizing investment income or crop-growing profitability, so I am at a loss.

Can anyone advise as to the form the spreadsheet should take? Thank you very much.