You are the mayor of Gotham City and you must determine a tax policy for the city. Five types of taxes are used to raise money: ■ Property taxes. Let p be the property tax rate. ■ A sales tax on all...

You are the mayor of Gotham City and you must determine a tax policy for the city. Five types of taxes are used to raise money:


■ Property taxes. Let p be the property tax rate.


■ A sales tax on all items except food, drugs, and durable goods. Let s be the sales tax rate.


■ A sales tax on durable goods. Let d be the durable goods sales tax rate.

■ A gasoline sales tax. Let g be the gasoline sales tax rate.


■ A sales tax on food and drugs. Let f be the sales tax on food and drugs.

The city consists of three groups of people: low income (LI), middle income (MI), and high income (HI). The amount of revenue (in millions of dollars) raised from each group by setting a particular tax at a 1% level is given in the file P09_41.xlsx. For example, a 3% tax on durable good sales will raise 360 million dollars from low-income people. Your tax policy must satisfy the following restrictions:


■ Restriction 1: The tax burden on MI people cannot exceed $2.8 billion.


■ Restriction 2: The tax burden on HI people cannot exceed $2.4 billion.


■ Restriction 3: The total revenue raised must exceed the current level of $6.5 billion.


■ Restriction 4: s must be between 1% and 3%.

Given these restrictions, the city council has set the following three goals (listed in order of priority):


■ Goal 1: Limit the tax burden on LI people to $2 billion.


■ Goal 2: Keep the property tax rate under 3%.


■ Goal 3: If their tax burden becomes too high, 20% of the LI people, 20% of the MI people, and 40% of the HI people may consider moving to the suburbs. Suppose that this will happen if their total tax burden exceeds $1.5 billion. To discourage this exodus, goal 3 is to keep the total tax burden on these people below $1.5 billion. Use goal programming to determine an optimal tax policy.