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 that can be covered from these locations are given in the following table: Potential Locations for Substations Areas Covered A 1, 2, 5, 7 B 1, 3, 5 C 2, 4, 5 D 3, 4, 6 E 4, 5, 6 F 1, 5, 6, 7 G 1, 5, 7 xA + xB + xC + xD + xE + xF + xG (area 1 covered) xA + xB + xC + xD + xE + xF + xG ≥, =, or less than or equal to (area 2 covered) xA + xB + xC + xD + xE + xF + xG (area 3 covered) xA + xB + xC + xD + xE + xF + xG (area 4 covered) xA + xB + xC + xD + xE + xF + xG (area 5 covered) xA + xB + xC + xD + xE + xF + xG (area 6 covered) xA + xB + xC + xD + xE + xF + xG (area 7 covered) (a) Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. Min xA + xB + xC + xD + xE + xF + xG s.t. xA + xB + xC + xD + xE + xF + xG (area 1 covered) xA + xB + xC + xD + xE + xF + xG (area 2 covered) xA + xB + xC + xD + xE + xF + xG (area 3 covered) xA + xB + xC + xD + xE + xF + xG less than or equal to, greater than or equal to, equal (area 4 covered) xA + xB + xC + xD + xE + xF + xG (area 5 covered) xA + xB + xC + xD + xE + xF + xG (area 6 covered) xA + xB + xC + xD + xE + xF + xG (area 7 covered) (b) Solve the problem in part (a). Choose the correct optimal solution. If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. Locations for Substations Select ? A B C D E F G
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 that can be covered from these locations are given in the following table: Potential Locations for Substations Areas Covered A 1, 2, 5, 7 B 1, 3, 5 C 2, 4, 5 D 3, 4, 6 E 4, 5, 6 F 1, 5, 6, 7 G 1, 5, 7 xA + xB + xC + xD + xE + xF + xG (area 1 covered) xA + xB + xC + xD + xE + xF + xG ≥, =, or less than or equal to (area 2 covered) xA + xB + xC + xD + xE + xF + xG (area 3 covered) xA + xB + xC + xD + xE + xF + xG (area 4 covered) xA + xB + xC + xD + xE + xF + xG (area 5 covered) xA + xB + xC + xD + xE + xF + xG (area 6 covered) xA + xB + xC + xD + xE + xF + xG (area 7 covered) (a) Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. Min xA + xB + xC + xD + xE + xF + xG s.t. xA + xB + xC + xD + xE + xF + xG (area 1 covered) xA + xB + xC + xD + xE + xF + xG (area 2 covered) xA + xB + xC + xD + xE + xF + xG (area 3 covered) xA + xB + xC + xD + xE + xF + xG less than or equal to, greater than or equal to, equal (area 4 covered) xA + xB + xC + xD + xE + xF + xG (area 5 covered) xA + xB + xC + xD + xE + xF + xG (area 6 covered) xA + xB + xC + xD + xE + xF + xG (area 7 covered) (b) Solve the problem in part (a). Choose the correct optimal solution. If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. Locations for Substations Select ? A B C D E F G
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 100P
Related questions
Question
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 that can be covered from these locations are given in the following table:
| Potential Locations for Substations |
Areas Covered |
| A | 1, 2, 5, 7 |
| B | 1, 3, 5 |
| C | 2, 4, 5 |
| D | 3, 4, 6 |
| E | 4, 5, 6 |
| F | 1, 5, 6, 7 |
| G | 1, 5, 7 |
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| (a) |
Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. |
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| Min | xA | + | xB | + | xC | + | xD | + | xE | + | xF | + | xG | ||||
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s.t.
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| (b) | Solve the problem in part (a). Choose the correct optimal solution. | ||||||||||||||||
| If your answer is zero enter “0” and if the constant is "1" it must be entered in the box. | |||||||||||||||||
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