A 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 upper class.

■ Goal 4: Raise at most $350 billion in taxes from the lower class.

Currently the government spends $1 trillion per year.

Revenue can be raised in two ways: through a gas tax and through an income tax. You must determine G, the per-gallon tax rate (in cents); T1, the tax rate charged on the first $30,000 of income; T2, the tax rate charged on any income earned over $30,000; and C, the cut in spending (in billions). If the government chooses G, T1, and T2, then we assume that the revenue given in the file P16_15.xlsx (in billions of dollars) is raised. Of course, the tax rate on income over $30,000 must be at least as large as the tax rate on the first $30,000 of income. Use goal programming to help the president meet his goals.