Question: Question 5: You are the Mayor of Gotham City (congratulations!), and you must determine a tax policy for the city. Five types of taxes are used to raise money:

• Property taxes. Let p denote the property tax percentage rate.

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

• A sales tax on durable goods. Let d denote the durable goods sales tax percentage rate

• A gasoline sales tax. Let g denote the gasoline sales tax percentage rate.

• A sales tax on food and drugs. Let f denote the sales tax percentage rate for food and drugs.

The city consists of 3 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 following table:

p s d g f

LI 900 300 120 30 90

MI 1200 400 100 20 60

HI 1000 250 60 10 40

For example, a 3% tax on durable goods will raise $360 million from low income people. Your tax policy must satisfy the following:

• The tax burden on MI people cannot exceed $2.8 billion

• The tax burden on HI people cannot exceed $2.4 billion

• The total revenue raised must exceed the current level of $6.5 billion

• s must be between 1% and 3%.

If possible, you would like to keep the property tax rate under 3%, and limit the tax burden on LI people to $2 billion.

Use linear programming to determine a tax policy.

Please answer using the proposed property tax percentage rate. (Input the percentage, not the fraction. Thus, 10% would be input as 10.)