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1,2,5,7 1,3,5

1,2,5,7 1,3,5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 Areas covered locations 1,5,7 1,2,5,7 1,3,5 2,4,5 E 3,4,6 4,5,6 1,5,6,7 There are two additional factors to be considered NOTE 1: At each of locations A through Ga 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, Fand G cost the least (treat the cost of opening a substation at C. D. F or Gas 1 unit), The cost to open at A is 7 times the cost at C(-7 units) and the cost to open at Bis 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 varlables simply as A, B. C, D, E, F and G (instead of XA, XB etc). Which of the following statements is true? O The decision varlables A, B, C. D. EFand Gare integer and can take on values 0, 1,2.3.4.5.. O The decision variables A. B. C. D, E.Fand Gcan be negative O The decision variables A. B. C. D. E.F and Gare binary and can only be O or 1 O The decison variables A, B. CD. E F and Gcan be fractional to allow for fractional coverage
Transcribed Image Text: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 Areas covered locations 1,5,7 1,2,5,7 1,3,5 2,4,5 E 3,4,6 4,5,6 1,5,6,7 There are two additional factors to be considered NOTE 1: At each of locations A through Ga 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, Fand G cost the least (treat the cost of opening a substation at C. D. F or Gas 1 unit), The cost to open at A is 7 times the cost at C(-7 units) and the cost to open at Bis 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 varlables simply as A, B. C, D, E, F and G (instead of XA, XB etc). Which of the following statements is true? O The decision varlables A, B, C. D. EFand Gare integer and can take on values 0, 1,2.3.4.5.. O The decision variables A. B. C. D, E.Fand Gcan be negative O The decision variables A. B. C. D. E.F and Gare binary and can only be O or 1 O The decison variables A, B. CD. E F and Gcan be fractional to allow for fractional coverage
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