ORIE 3300/5300
ASSIGNMENT 3
Fall 2008
Individual work.
Due: 3 p.m., Friday September 26.
1. Part of next week’s recitation concerns the “Diet” linear programming
model. In preparation, read pages 27–36 in the AMPL book. Also
review pages 16–18.
2. Below is a picture of the feasible region for the following linear pro
gram.
maximize
2
x
1
+
3
x
2
+
x
3
subject to
x
1
≤
2
x
2
≤
2

x
1
+
x
3
≤
2
x
1
+
x
2
≤
3
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, always choose the one
with the smallest index at each iteration. 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?
1
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View Full Document3. The following is a tableau for a linear program in standard equality
form.
z
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 Fall '08
 TODD
 Linear Programming, Optimization, objective function value, nonbasic variables, x1 + x2

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