Question

1. Huntington is considering have police sub-stations to provide better coverage of the city. There are six (6) areas in the city. There are five possible locations for sub-stations. Given the data below, formulate the integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas.

Potential Locations                             Areas Covered

                                    A                                                         1, 5

                                    B                                                         2, 3, 5, 6         

                                    C                                                         1, 4

                                    D                                                         1, 2, 4, 6

                                    E                                                          4, 5

Answer 1

Answer:-

Given That:-

Huntington is considering have police sub-stations to provide better coverage of the city. There are six (6) areas in the city. There are five possible locations for sub-stations. Given the data below, formulate the integer programming model that could be used to

find the minimum number of locations necessary to provide coverage to all areas.?

The Huntington is considering 5 police sub-stations to provide better coverage of the 6 areas of city.

Potential Locations Areas Covered

                                    A 1, 5

                                    B 2, 3, 5, 6         

                                    C 1, 4

                                    D 1, 2, 4, 6

                                    E 4, 5

The matrix is the coverage as follow

	1	2	3	4	5	6
A B C D E	1 0 1 1 0	0 1 0 1 0	0 1 0 0 0	0 0 1 1 1	1 1 0 0 1	0 1 0 1 0

here,

The formulation of given integers problem is As min

For Area :-

For Area:-

For Area:-

For Area:-

For Area:-

For Area:-