ANSWER USING LINGO WILL DOWNVOTE FOR ANSWER USING EXCEL SOLVER!!

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 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. Y { 6 otherwisent is built in community i } i=1,...,9. ={ 1 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. (6) Solve the model using LINGO or the Excel Solver. (c) State the solution in words