OPTIMIZATION & SPREADSHEET MODELING / MANAGEMENT SCIENCE

Grave city is considering the relocation of several police substations to obtain better enforcement in high crime areas. The locations under consideration together with the areas covered (7 areas in total) are tabulated below:

Potential substation locations	Areas covered
A	1,5,7
B	1,2,5,7
C	1,3,5
D	2,4,5
E	3,4,6
F	4,5,6
G	1,5,6,7

There are two additional factors to be considered:

NOTE 1: At each of locations A through G a police substation can be located or not. Moreover, the cost of opening a substation at a particular substation differs from A through G. The locations at C, D, F and G cost the least (treat the cost of opening a substation at C, D, F, or G as 1 unit). The cost to open at A is 7 times the cost at C (= 7 units) and the cost to open at B is thrice the cost at C (= 3 units). The cost to open at E is 4 units.

NOTE 2: Areas 1, 4, and 7 are high crime areas. In particular, area 1 requires two separate substations to cover it, area 4 requires 3 substations to cover it and area 7 also requires 2 separate substations to cover it.

We will denote the decision variables simply as A, B, C, D, E, F, and G (instead of X_A, X_B, etc).

Which of the following statements is true?

Group of answer choices

A. The decision variables A, B, C, D, E, F and G can be negative

B. The decision variables A, B, C, D, E, F and G are integer and can take on values 0, 1, 2 , 3, 4,5...

C. The decision variables A, B, C, D, E, F and G are binary and can only be 0 or 1.

D. The decision variables A, B, C, D, E, F and G can be fractional to allow for fractional coverage