A mathematical problem should be difficult to entice us, yet not completely inaccessible. It should be a guidepost on the mazy paths to hidden truths. – David Hilbert
In a space-limited outdoor diner we visited a while ago, we observed the seating arrangement in A. They had two tables for two and ten for four. Seven of the four-place tables had parties of two. So, I wondered – is the setup they had the best for the crowd they faced?
A report I found (see below) noted that restaurant parties of two outnumber four-person parties by over two to one. On average, there should be more tables set up for couples than for larger groups.
But the average condition may not be the usual one. Or the one they faced.
What to do?
Suppose the four left-most tables were modular. The establishment could separate them into eight two-place setups. Then they could seat all seven of their two-person parties and put a two-top in storage. Their capacity would go down by two (at least temporarily), but, in the case shown, occupancy could go up by 30%, as we see in B.
Restaurants make money through occupancy, not capacity. It’s important to know what problem you need to solve.