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 P16_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.