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: Community 1 2 3 4 5 6 7 8 9 Population (000's) 38 15 13 R = number of restaurants built. 22 11 31 9 24 23 N = population (in thousands) of communities with a restaurant. N =population (in thousands) of communities without a restaurant of their own but which are contiguous to a community which does have a restaurant. Y {arreraient is built in community i otherwise '} i=1,...,9. 1 a restaurant is not built in community i, but Zi a restaurant is built in a contiguous community 0 otherwise i=1,...,9. (a) Follow page 1 part (d). For this question only, you do not have to include the variable definitions. (b) Solve the model, and state the solution in words.