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's 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

TABLE 77

    

	p	s	d	g	f
LI	900	300	120	30	90
MI	1,200	400	100	20	60
HI	1,000	250	60	10	40