ORIE 3300/5300
ASSIGNMENT 3
Fall 2011
Individual work.
Due: 11am, Tuesday September 20.
1. Next week’s recitation concerns the “Diet” linear programming model.
In preparation, read pages 27–35 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. 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?
Now try solving the new problem obtained by replacing the objective
function
x
1
+ 2
x
2
+
x
3
by
x
1
+
x
2
+
x
3
. This time, at each iteration,
1
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 '10
 TODD
 Linear Programming, Optimization, linear program, possible entering variables

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