Widget Co wants to open a number of stores in different cities Since a store in a city can serve nearby cities to some degree Widget Co wonders if they can open stores in only some cities They want to minimize the total cost of opening stores but cover 100 of the population A sore covers that opens in a city covers 100 of the population in that city and 25 of the population in a nearby city If a city have four stores opened in nearby cities 100 of the population in that city is covered If a store is opened in a nearby city, 25 of the population goes to that store If stores in two nearby cities are opened 25 of the population goes to one of the stores and 25 goes to another for a total of 50 If stores are opened in four nearby cities 100 of the population in the city goes to a store and if more than four stores are opened in nearby cities no more than 100 of the population goes to a store The cost of open a store and what cities are nearby can be read of in the table below City Nearby cities Cost A LN 30410 BKDGH 36582 CIME 30444 D BEGHK 49379 E DKH 31960 F CM 31383 GBDHIK 41887 HBDEGK 47951 I CGMO 42472 JIMO 39737 LAN 29764 K BDEGH 46729 M ICF 40912 NAL 34174 OT 33645 Formulate a binary model helping Widget Co to decide in which cities to open stores so that 100 of the population goes to at least one store and the total cost of opening stores are minimized (6p)

Question

Widget   Co  wants to open a number of stores in different cities  Since a store in a city can serve nearby cities to some degree Widget   Co  wonders if they can open stores in only some cities  They want to minimize the total cost of opening stores but cover 100  of the population  A sore covers that opens in a city covers 100  of the population in that city and 25  of the population in a nearby city  If a city have four stores opened in nearby cities 100  of the population in that city is covered  If a store is opened in a nearby city, 25  of the population goes to that store  If stores in two nearby cities are opened 25  of the population goes to one of the stores and 25  goes to another for a total of 50   If stores are opened in four nearby cities 100  of the population in the city goes to a store and if more than four stores are opened in nearby cities no more than 100  of the population goes to a store  The cost of open a store and what cities are nearby can be read of in the table below  City Nearby cities Cost A LN 30410 BKDGH 36582 CIME 30444 D BEGHK 49379 E DKH 31960 F CM 31383 GBDHIK 41887 HBDEGK 47951 I CGMO 42472 JIMO 39737 LAN 29764 K BDEGH 46729 M ICF 40912 NAL 34174 OT 33645 Formulate a binary model helping Widget   Co  to decide in which cities to open stores so that 100  of the population goes to at least one store and the total cost of opening stores are minimized  (6p)

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Widget & Co. wants to open a number of stores in different cities. Since a store in a city can serve nearby cities to some

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