The new president has just been elected and has set the following economic goals (listed from highest to lowest priority):
Goal 1 Balance the budget (this means revenues are at least as large as costs).
Goal 2 Cut spending by at most $150 billion.
Goal 3 Raise at most $550 billion in taxes from the rich.
Goal 4 Raise at most $350 billion in taxes from the poor.
Currently, the government spends $1 trillion (a trillion = 1,000 billion) per year. Revenue can be raised in two ways:
through a gas tax and an income tax. You must determine
G = per gallon tax rate (in cents)
LTR = % tax rate charged on first $30,000 of income
HTR = % tax rate charged on any income earned more than $30,000
C = cut in spending (in billions)
If the government chooses G, LTR, and HTR, then the revenue given in Table (in billions) is raised.
|
Low Income
|
High Income
|
|
Gas tax
|
G
|
.5G
|
|
Tax on income up to $30,000
|
20LTR
|
5LTR
|
|
Tax on income above $30,000
|
0
|
15HTR
|
Of course, the tax rate on income more than $30,000 must be at least as large as the tax rate on the first $30,000 of income. Formulate a preemptive goal programming model to help the president meet his goals.