Please help to work on (a), (b), (c), (d). Thank you

B D E F G H I J K L A 1 Distance Matrix (miles) 2 County 3 Lake, IL 4 McHenry, IL 5 Cook, IL 6 DuPage, IL 7 Kane, IL 8 Will, IL 9 Kendall, IL 10 Kankakee, IL 11 Grundy, IL 12 Lake, IN 13 14 County 15 Annual Cost of a centre (for Q4d) 16 Lake, IL McHenry, IL Cook, IL DuPage, IL Kane, IL Will, IL Kendall, IL Kankakee, IL Grundy, IL Lake, IN Demand 0 19 35 32 33 55 52 82 72 62 64435 19 0 44 34 26 56 45 84 68 73 26008 35 44 0 16 301 25 36 49 48 29 537674 32 34 16. 0 14 23 24. 51 41 41 90416 33 26 30 14 0 31 19. 60 42 55 40412 55 56 25 23 31 0 22 29 23 33 50227 52 45 36 24 19 22 0 46 24 54 5454 82 49 60 29 46 0 29 10383 72 68 48 41 42 23 24 29 0 53 3754 62 73 29 41 55 33 54 36 53 0 48457 0 Lake, IL McHenry, IL Cook, IL DuPage, IL Kane, IL Will, IL Kendall, IL Kankakee, IL Grundy, IL Lake, IN 6728160 4815270 1035950 7070760 4426350 7433040 2653000 4077890 7188790 2996610 84 36. The worksheet of Q3 in Assignment1Data.xlsx provides data about the 10 counties around Chicago. The data are used for all of the following questions. a. [10 marks] The government is planning to set up emergency facilities in some of the counties. They have to ensure that each county has at least one emergency facility within a distance of 20 miles. What is the minimum number of facilities required? b. [10 marks] Consider the same situation as in part a and the government can establish at most three emergency facilities. If the coverage distance is still 20 miles, where should the facilities be located to maximize the total demand covered? c. [10 marks] The government is planning to set up four community centres in some of the counties. In a view to promoting more convenient access for the citizens, they wish to minimize the demand-weighted total distance from the counties to their nearest centres. Where should the centres be located? d. [10 marks] The government is planning to set up several healthcare centres in some of the counties for the provision of homecare services to citizens. The annual cost of opening a centre in each county is provided in the worksheet of Q3 in Assignment1 Data.xlsx. It is given that the travel cost per mile per case is $1, where the demand in the file is the expected number of cases in each county in a year. How many facilities should be opened? e. [20 marks] A company is planning to open three big shopping malls in some of the counties. They learned that there are already three similar shopping malls in Cook, IL, Will, IL, and Lake, IN (one for each). Suppose that the closest shopping mall fully captures the demand of each county; but if two shopping malls have the same distance to the county, the demand will be equally shared by both. Where should the company open the three shopping malls to maximize the total demand captured? [Hint: You will need to develop a new location model based on some model(s) you learned in the lectures. Additional decision variables to determine if the amount of demand is fully or partially (if half) captured are needed.] B D E F G H I J K L A 1 Distance Matrix (miles) 2 County 3 Lake, IL 4 McHenry, IL 5 Cook, IL 6 DuPage, IL 7 Kane, IL 8 Will, IL 9 Kendall, IL 10 Kankakee, IL 11 Grundy, IL 12 Lake, IN 13 14 County 15 Annual Cost of a centre (for Q4d) 16 Lake, IL McHenry, IL Cook, IL DuPage, IL Kane, IL Will, IL Kendall, IL Kankakee, IL Grundy, IL Lake, IN Demand 0 19 35 32 33 55 52 82 72 62 64435 19 0 44 34 26 56 45 84 68 73 26008 35 44 0 16 301 25 36 49 48 29 537674 32 34 16. 0 14 23 24. 51 41 41 90416 33 26 30 14 0 31 19. 60 42 55 40412 55 56 25 23 31 0 22 29 23 33 50227 52 45 36 24 19 22 0 46 24 54 5454 82 49 60 29 46 0 29 10383 72 68 48 41 42 23 24 29 0 53 3754 62 73 29 41 55 33 54 36 53 0 48457 0 Lake, IL McHenry, IL Cook, IL DuPage, IL Kane, IL Will, IL Kendall, IL Kankakee, IL Grundy, IL Lake, IN 6728160 4815270 1035950 7070760 4426350 7433040 2653000 4077890 7188790 2996610 84 36. The worksheet of Q3 in Assignment1Data.xlsx provides data about the 10 counties around Chicago. The data are used for all of the following questions. a. [10 marks] The government is planning to set up emergency facilities in some of the counties. They have to ensure that each county has at least one emergency facility within a distance of 20 miles. What is the minimum number of facilities required? b. [10 marks] Consider the same situation as in part a and the government can establish at most three emergency facilities. If the coverage distance is still 20 miles, where should the facilities be located to maximize the total demand covered? c. [10 marks] The government is planning to set up four community centres in some of the counties. In a view to promoting more convenient access for the citizens, they wish to minimize the demand-weighted total distance from the counties to their nearest centres. Where should the centres be located? d. [10 marks] The government is planning to set up several healthcare centres in some of the counties for the provision of homecare services to citizens. The annual cost of opening a centre in each county is provided in the worksheet of Q3 in Assignment1 Data.xlsx. It is given that the travel cost per mile per case is $1, where the demand in the file is the expected number of cases in each county in a year. How many facilities should be opened? e. [20 marks] A company is planning to open three big shopping malls in some of the counties. They learned that there are already three similar shopping malls in Cook, IL, Will, IL, and Lake, IN (one for each). Suppose that the closest shopping mall fully captures the demand of each county; but if two shopping malls have the same distance to the county, the demand will be equally shared by both. Where should the company open the three shopping malls to maximize the total demand captured? [Hint: You will need to develop a new location model based on some model(s) you learned in the lectures. Additional decision variables to determine if the amount of demand is fully or partially (if half) captured are needed.]