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 #4
Due Tuesday, February 2
1.
Solve the following system of equations using the pivot method.
5
x
1
+ 3
x
2
= 10
−
x
1
+ 2
x
2
= 6
Show the BASIS of this system. Report the solution and the inverse of the basis.
2. Solve the following system of equations using the pivot method.
5
x
1
+ 3
x
2
−
4
x
3
= 20
−
x
1
+ 2
x
2
+ 3
x
3
= 18
3
x
1
−
2
x
2
+ 5
x
3
= 21
Report the solution and the inverse of the basis.
3.
Consider the following LP problem:
max
TR
= 5
x
1
+ 6
x
2
+ 3
x
3
subject to
5
x
1
+ 3
x
2
+ 4
x
3
≤
10
−
x
1
+ 2
x
2
−
3
x
3
≤
6
x
j
≥
0
, j
= 1
, . . . ,
3
.
A) Solve the above LP problem by hand using the PRIMAL SIMPLEX algorithm.
B) Exhibit the complete primal and dual solutions, the optimal value of the
objective function and identify the optimal primal and dual bases.
C) Now solve the same primal problem using Microsoft Excel and compare the
solutions obtained in A) and in C). Print out that file. Give a complete report. In
other words, you must report 1) the optimal value of the objective function, 2) the
entire primal optimal solution (including the primal slack variables), 3) the entire
dual solution (including the dual slack variables).
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