(a) Using the variables as defined above, write the objective function and the constraints for this problem. (b) Solve the model using LINGO or Excel Solver. (c) State the solution in words.

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 fast-food 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 profit of $50. The population of each community is: 4 5 6 Community 1 Population (000's) 5 8 12 23 8 16 30 4 34 R = number of restaurants built. N1 = 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. Find annual conibution to pront of OSU. The population of each community 15. Community 1 Population (000's) 5 23 23 8 4 16 5 30 6 4 7 34 8 12 R = number of restaurants built. Ni = population (in thousands) of communities with a restaurant. Ny = 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 0 otherwise i=1,...,8. Z 1 a restaurant is not built in community i, but a restaurant is built in a contiguous community 0 otherwise i=1,...,8