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ASSIGNMENT 3
Fall 2010
Individual work.
Due: 3 pm, Friday September 24.
1. Next week’s recitation concerns the “Diet” linear programming model. In
preparation, read pages 27–36 in the AMPL book.
2. Below is a picture of the feasible region for the following linear program.
maximize
x
1
+
2
x
2
+
x
3
subject to
x
1
≤
3
x
2
≤
3
x
1
+
x
2
≤
4

x
1
+
x
3
≤
1
x
1
,
x
2
,
x
3
≥
0
.
Solve the linear program using the simplex method. First introduce slack
variables, and use them as the basic variables in an initial feasible tableau.
Among the possible entering variables, choose one with largest reduced
cost at each iteration; if there is a choice, pick among these the one with
the smallest index. Plot the path taken by the simplex method on the
picture. Does your ﬁnal tableau imply that the optimal solution is unique?
If not, can you ﬁnd another optimal solution?
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This note was uploaded on 11/11/2010 for the course ORIE 3300 at Cornell University (Engineering School).
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