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4. (25 marks) There are nine communities located along the coast of an island, all con- nected via a coastal road. Numbered in succession 1 to 9, community 1 is contigu- ous with communities 2 and 9, and community 9 is contiguous with communities 8 and 1. A chain of fish and chips restaurants is considering opening a restaurant in as many as three of the nine communities. They believe that they will capture 25% of the market in those communities in which a restaurant is constructed. Furthermore, they believe that they will capture 10% of the market in any community which does not have its own restaurant but which is contiguous to a community (on either or both sides) which does have a restaurant. Each restaurant would have an annual overhead cost of $250,000. Each customer would give an annual contribution to profit of $60. The population of each community is: Business 2400, Winter 2021, written by Dr. David M. Tulett 4 Community 1 2 3 4 5 6 7 8 9 Population (000's) 38 15 13 22 11 31 9 24 23 R = number of restaurants built. Ni = population (in thousands) of communities with a restaurant. N2 = population in thousands) of communities without a restaurant of their own but which are contiguous to a community which does have a restaurant. 1 a restaurant is built in community i Y; { colher wise } i 1,...,9. I a restaurant is not built in community i, but Z a restaurant is built in a contiguous community i=1,...,9. 0 otherwise (a) Using the variables as defined above, write the objective function and the con- straints for this problem. You are not required to submit this part. (b) Solve the model using LINGO or the Excel Solver. (c) State the solution in words. 4. (25 marks) There are nine communities located along the coast of an island, all con- nected via a coastal road. Numbered in succession 1 to 9, community 1 is contigu- ous with communities 2 and 9, and community 9 is contiguous with communities 8 and 1. A chain of fish and chips restaurants is considering opening a restaurant in as many as three of the nine communities. They believe that they will capture 25% of the market in those communities in which a restaurant is constructed. Furthermore, they believe that they will capture 10% of the market in any community which does not have its own restaurant but which is contiguous to a community (on either or both sides) which does have a restaurant. Each restaurant would have an annual overhead cost of $250,000. Each customer would give an annual contribution to profit of $60. The population of each community is: Business 2400, Winter 2021, written by Dr. David M. Tulett 4 Community 1 2 3 4 5 6 7 8 9 Population (000's) 38 15 13 22 11 31 9 24 23 R = number of restaurants built. Ni = population (in thousands) of communities with a restaurant. N2 = population in thousands) of communities without a restaurant of their own but which are contiguous to a community which does have a restaurant. 1 a restaurant is built in community i Y; { colher wise } i 1,...,9. I a restaurant is not built in community i, but Z a restaurant is built in a contiguous community i=1,...,9. 0 otherwise (a) Using the variables as defined above, write the objective function and the con- straints for this problem. You are not required to submit this part. (b) Solve the model using LINGO or the Excel Solver. (c) State the solution in words