This problem is based on the following research article that you must read. "Multi-objective Linear programming Methodology for Public Sector Tax Planning," by James Chrisman, Timothy Fry, Gary Reeves, Holly Lewis, and Robert Weinstein, Interfaces Vol. 19, No. 5, (1989) pp. 13 – 30. Suppose that you have been hired by the city council of Peoria, Illinois to help them meet their overall tax goals. Suppose the city government came up with the following four goals listed below in order of descending of priority: Limit the tax burden on Lower Income (LI) people to 1.75 billion. 1. Keep the property tax rate at 1%. 2. Minimize the "flight to the suburbs" by keeping the tax burden on Middle Income (MI) people 3. less than $2.5 billion and keeping the tax burden on High Income (HI) people to less than 2.25 billion. Try to eliminate the food and drug sales tax if possible. 4. The city currently levies five types of taxės: (a) property taxes (where p is the tax rate). (b) sales tax on general items except on food and drug and durable goods (where s is the general tax rate), (c) sales tax on food and drugs), (d) sales tax on durable goods (d is the sales tax on durable goods), and (e) gasoline tax (g is the gasoline tax rate). Relevant information on revenue generated by a 1% tax is provided in the table seen below Food & Drug Income Level Sales Durable Gasoline Property Low (LI) Middle (MI) High (HI) 300 200 50 120 400 450 125 30 80 1500 150 80 15 60 1200 Assume that 10% of the LI people will move out of the city into the suburbs if their tax burden exceeds 1.75 billion, 20% of MI people will move out of the city into the suburbs if their tax burden exceeds 2.5 billion, and 30% of HI people will move out of the city into the suburbs if their tax burden exceeds 1.25 billion. You must work within the following "hard" constraints: The sales tax must be between 1% and 3%, as indicated in the accompanying research article. The total revenue raised must exceed the current level of $6.0 billion. The tax burden on the HI people can't exceed $1.5 billion The tax burden on the MI people can't exceed 3.0 billion Build an Excel Model to model the problem and answer the following questions (provide a model template of each question). (a) Use goal programming proposed in the article to formulate this model (hint: you can learn from and modify the model of the article to answer this question).
(b) From your proposed model solution, stated which goals can be satisfied?