To encourage the adoption of electric vehicles (EV), the transport au- thorities launched a plan to...

 

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To encourage the adoption of electric vehicles (EV), the transport au- thorities launched a plan to install EV charging stations within public car parks in the central region of Singapore. A total of 12 existing car parks have been identified as potentially suitable for installing this initial first batch of charging stations. To enable this limited charg- ing network to have extensive reach throughout the region but in an economical manner, the authorities would like to install charging sta- tions in as many of these 12 car parks as possible but at the same time ensure that the car parks selected for installation are well spread out throughout the region without having two or more of the selected car parks located too near each other. Hence each car park selected for installation must be at least Dmin 2 km away from any other selected car park. The location of each of the 12 car parks is known and spec- ified by its respective (X;, Y.) positional coordinates measured in km with respect to some reference point, for i = 1, 2, 3,..., 12, as tabulated below. Which are the car parks that should be selected for installation of the charging stations? = i 1 2 3 4 5 6 7 9 10 11 12 X 2.5 5.0 8.0 3.5 7.5 6.5 4.0 7.0 3.0 8.0 6.0 1.5 Y 1.0 1.5 1.5 2.0 3.0 3.5 6.0 6.5 7.5 7.5 8.0 8.5 The above problem is to be solved in advance as a trial for preparing the spreadsheet before the quiz. During the quiz, the same problem needs to be solved again based on all the same parameters except for the possibly different set of values that will be given in the quiz question for Dmin and the coordinates of the car parks (X, Y), i = 1,2,3,..., 12. To encourage the adoption of electric vehicles (EV), the transport au- thorities launched a plan to install EV charging stations within public car parks in the central region of Singapore. A total of 12 existing car parks have been identified as potentially suitable for installing this initial first batch of charging stations. To enable this limited charg- ing network to have extensive reach throughout the region but in an economical manner, the authorities would like to install charging sta- tions in as many of these 12 car parks as possible but at the same time ensure that the car parks selected for installation are well spread out throughout the region without having two or more of the selected car parks located too near each other. Hence each car park selected for installation must be at least Dmin 2 km away from any other selected car park. The location of each of the 12 car parks is known and spec- ified by its respective (X, Y) positional coordinates measured in km with respect to some reference point, for i= 1, 2, 3,..., 12, as tabulated below. Which are the car parks that should be selected for installation of the charging stations? = i 1 2 3 4 5 6 7 9 10 11 12 X 2.5 5.0 8.0 3.5 7.5 6.5 4.0 7.0 3.0 8.0 6.0 1.5 Y 1.0 1.5 1.5 2.0 3.0 3.5 6.0 6.5 7.5 7.5 8.0 8.5 The above problem is to be solved in advance as a trial for preparing the spreadsheet before the quiz. During the quiz, the same problem needs to be solved again based on all the same parameters except for the possibly different set of values that will be given in the quiz question for Dmin and the coordinates of the car parks (X, Y), i = 1,2,3,..., 12. To encourage the adoption of electric vehicles (EV), the transport au- thorities launched a plan to install EV charging stations within public car parks in the central region of Singapore. A total of 12 existing car parks have been identified as potentially suitable for installing this initial first batch of charging stations. To enable this limited charg- ing network to have extensive reach throughout the region but in an economical manner, the authorities would like to install charging sta- tions in as many of these 12 car parks as possible but at the same time ensure that the car parks selected for installation are well spread out throughout the region without having two or more of the selected car parks located too near each other. Hence each car park selected for installation must be at least Dmin 2 km away from any other selected car park. The location of each of the 12 car parks is known and spec- ified by its respective (X;, Y.) positional coordinates measured in km with respect to some reference point, for i = 1, 2, 3,..., 12, as tabulated below. Which are the car parks that should be selected for installation of the charging stations? = i 1 2 3 4 5 6 7 9 10 11 12 X 2.5 5.0 8.0 3.5 7.5 6.5 4.0 7.0 3.0 8.0 6.0 1.5 Y 1.0 1.5 1.5 2.0 3.0 3.5 6.0 6.5 7.5 7.5 8.0 8.5 The above problem is to be solved in advance as a trial for preparing the spreadsheet before the quiz. During the quiz, the same problem needs to be solved again based on all the same parameters except for the possibly different set of values that will be given in the quiz question for Dmin and the coordinates of the car parks (X, Y), i = 1,2,3,..., 12. To encourage the adoption of electric vehicles (EV), the transport au- thorities launched a plan to install EV charging stations within public car parks in the central region of Singapore. A total of 12 existing car parks have been identified as potentially suitable for installing this initial first batch of charging stations. To enable this limited charg- ing network to have extensive reach throughout the region but in an economical manner, the authorities would like to install charging sta- tions in as many of these 12 car parks as possible but at the same time ensure that the car parks selected for installation are well spread out throughout the region without having two or more of the selected car parks located too near each other. Hence each car park selected for installation must be at least Dmin 2 km away from any other selected car park. The location of each of the 12 car parks is known and spec- ified by its respective (X, Y) positional coordinates measured in km with respect to some reference point, for i= 1, 2, 3,..., 12, as tabulated below. Which are the car parks that should be selected for installation of the charging stations? = i 1 2 3 4 5 6 7 9 10 11 12 X 2.5 5.0 8.0 3.5 7.5 6.5 4.0 7.0 3.0 8.0 6.0 1.5 Y 1.0 1.5 1.5 2.0 3.0 3.5 6.0 6.5 7.5 7.5 8.0 8.5 The above problem is to be solved in advance as a trial for preparing the spreadsheet before the quiz. During the quiz, the same problem needs to be solved again based on all the same parameters except for the possibly different set of values that will be given in the quiz question for Dmin and the coordinates of the car parks (X, Y), i = 1,2,3,..., 12.

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