29 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:

a Property taxes. Let p property tax percentage rate.

b A sales tax on all items except food, drugs, and durable goods. Let s sales tax percentage rate.

c A sales tax on durable goods. Let d durable goods sales tax percentage rate.

d A gasoline sales tax. Let g gasoline tax sales percentage rate.

e A sales tax on food and drugs. Let f 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 Table 77.

For example, a 3% tax on durable good sales will raise

$360 million from low-income people. Your tax policy must satisfy the following:

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 mayor has set the following three goals:

Goal P Keep the property tax rate less than 3%.

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

Goal Suburbs 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, the suburb goal is to keep the total tax burden on these people below $1.5 billion.

Use goal programming to determine an optimal tax policy if the mayor’s goals follow the following set of priorities LI>>> P>>> Suburbs†

Transcribed Image Text:

TABLE 77 f LI 900 300 120 MI 1,200 400 100 HI 1,000 250 2880 30 20 60 10 2290 90 60 40