I am not a mathematician so please correct me if I am making any mistakes while explaining my problem (and please help me set the right tags as well because I am not sure what class of problem I am facing). While trying to solve it, I am also trying to frame the right question.

From some mobility data that I collected from an experiment I was conducting, I plotted the following spatial distribution graph for the area that I am analyzing. For about 30 people, this graph gives a distribution of how long each person spent in the area (which is a plane with dimensions 200x200). So for instance, over the period of observation (18 hours), the upper-left is the most visited region.

I am trying to place an experimental delivery service that has a proximity of 40m (circle) in the region is a way that it covers the maximum density region. The idea is that I have only a limited amount of resources and need to make the best use of them i.e. within the 40m proximity I should be able to cover the maximum number of people during the observation period.

I am guessing that my problem is not a new one and was hoping if someone could guide me in the right direction of understanding and solving this problem.