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 2011 by Quirino Paris.
ARE 155
Winter 2011
Prof. Quirino Paris
HOMEWORK #1
Due Tuesday, January 11
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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 Spring '08
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 Economics, Marginal rate, objective function, Quirino Paris, Prof. Quirino Paris

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