13 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 68 (in billions) is raised. 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.