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# Algebra - Linear Operators

According to http://www.whitehouse.gov/omb/budget/fy2006/tables.html, the U.S. government received approximately \$2 trillion in funds during the year 2005. Approximately \$1.3 trillion had already been promised to programs such as Medicare and Social Security, leaving approximately \$700 billion in "discretionary" funds for budget items like defense and education.

Suppose the Department of Defense required at least \$440 billion to function and that the total spending by other government departments (Education, Health and Human Services, Food and Drug Administration, Energy, etc.) was required to be at least \$480 billion.
Suppose further that every \$100 billion spent on defense increased taxpayer satisfaction by 5% while every \$100 billion spent on other services increased satisfaction by 3%.

1. Formulate a linear programming problem to maximize taxpayer satisfaction subject to the constraints on discretionary spending.
2. Graph the constraints as when finding the feasible region
3. Can you find a solution that maximizes taxpayer satisfaction? Why or why not?

#### Solution Summary

The following posting helps with problems involving linear programming, graphing constraints and maximizing taxpayer satisfaction. Neat and step-wise soltuions are provided. A graph is provided as well.

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