i	Xi	Yi
1	3	4
2	15	4
3	6	5
4	13	6
5	7	7
6	16	8
7	3	10
8	12	12
9	4	13
10	15	14
11	2	15
12	17	17

Don't have to solve the problem. Just formulate an objective function and constraints functions will do.

In order to quickly roll out a vaccination programme to protect the residents of a city against Covid-19, the health authorities identified 12 existing community centres (CCs) that can potentially be converted into vaccination centres (VCs). To provide the optimal capacity and convenience to the residents all over the city, the authorities would like to convert as many CCs into VCs as possible but at the same time ensure the VCs are well spread out throughout the city without having two or more VCs located too near each other. Hence the CCs selected for conversion must be such that each selected CC is at least Dmin=4km away from any other selected CC. The location of each of the 12 CCs is known and specified by its respective (Xi,Yi) positional coordinates measured in km with respect to some reference point, for i=1,2,3,,12, as tabulated below. Which are the CCs that should be selected for conversion? 1. As the problem is to determine whether any particular CC is selected or not, binary variables may be appropriate for use in this problem. 2. For easier identification of the various quantities and variables involved, they should be organized systematically within the spreadsheet, with meaningful namesotation used to label each of them. A smart arrangement of these quantities will also help in a more efficient input of the many formulae needed in the spreadsheet. 3. With the relatively large number of (binary) design variables in this problem, there is a likelihood of the optimization process getting trapped in a local optimum. For a higher chance of finding the global optimum, alternative initial design variable values may have to be used to run the process multiple times (hint : the global optimum can more likely be obtained by starting with initial values defining all the CCs as being selected and allowing the optimization process to de-select some of the CCs and converge to a feasible and optimal solution). In order to quickly roll out a vaccination programme to protect the residents of a city against Covid-19, the health authorities identified 12 existing community centres (CCs) that can potentially be converted into vaccination centres (VCs). To provide the optimal capacity and convenience to the residents all over the city, the authorities would like to convert as many CCs into VCs as possible but at the same time ensure the VCs are well spread out throughout the city without having two or more VCs located too near each other. Hence the CCs selected for conversion must be such that each selected CC is at least Dmin=4km away from any other selected CC. The location of each of the 12 CCs is known and specified by its respective (Xi,Yi) positional coordinates measured in km with respect to some reference point, for i=1,2,3,,12, as tabulated below. Which are the CCs that should be selected for conversion? 1. As the problem is to determine whether any particular CC is selected or not, binary variables may be appropriate for use in this problem. 2. For easier identification of the various quantities and variables involved, they should be organized systematically within the spreadsheet, with meaningful namesotation used to label each of them. A smart arrangement of these quantities will also help in a more efficient input of the many formulae needed in the spreadsheet. 3. With the relatively large number of (binary) design variables in this problem, there is a likelihood of the optimization process getting trapped in a local optimum. For a higher chance of finding the global optimum, alternative initial design variable values may have to be used to run the process multiple times (hint : the global optimum can more likely be obtained by starting with initial values defining all the CCs as being selected and allowing the optimization process to de-select some of the CCs and converge to a feasible and optimal solution)