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are155-homework-1

are155-homework-1 - University of California Davis...

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University of California, Davis Department of Agricultural and Resource Economics “We are what we repeatedly do. Excellence then is not an act, but a habit.” Aristotle Copyright c 2010 by Quirino Paris. ARE 155 Winter 2010 Prof. Quirino Paris HOMEWORK #1 Due Tuesday, January 12 1. a. Solve the following system of equations by any method known to you: 3 x 1 x 2 + 2 x 3 = 1 x 1 + 3 x 3 = 2 4 x 1 + 2 x 3 = 3 Check your answer by showing that your solution satisfies each equation. Practice solving systems of equations with numerical examples of your choice. Begin with systems of 2 equations and 2 unknowns and then solve 3 × 3 systems of equations. (You can consult a textbook of linear algebra.) b. In your words, briefly explain the meaning of solving a system of equations. c. Give the geometrical meaning of solving a system of equations. There are two geometrical meanings. d. Graphically solve the following system of inequalities (display the entire solu- tion region on a carefully drawn graph; label the axes): x 1 + 3 x 2 6 4 x 1 + 2 x 2 8 x 1 0 x 2 0 and, in your words, explain the meaning of solving a system of inequalities. 2. Graphically solve the following system of inequalities (label the axes) 2 x 1 + x 2 4 3 x 1 x 2 5 x 1 0 (be careful to draw the correct direction of the inequalities). Practice graphing sys- tems of inequalities with numerical examples of your choice. 1
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3. Solve the following LP problem by graphical methods (label the axes). Be as accurate as possible. Choose the “right” scale for your axes.
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