4. (25 marks) There are eight communities located along the Trans-Canada High way, with community 1 being the most westerly, and community 8 being the most easterly. Currently, none of the eight communities has a fast-food restaurant. A fastfood restaurant chain is considering opening up to four restaurants in the eight communities (no more than one restaurant per community). They believe that they will capture 30% of the market in those communities in which a restaurant is con- structed. Furthermore, they believe that they will capture 15% 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 $200,000. Each customer would give an annual contribution to prot of $50. The population of each community is: IIIIIE3III Population (000's) 16 30 R = number of restaurants built. N1 2 population (in thousands) of communities with a restaurant. N2 2 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,- = . l = 1, . . . ,8. 0 otherwrse I 1 a restaurant is not built in community i, but 1 a Z,- = a restaurant is built in a contiguous community ' = 1,. . . ,8