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ORIE 3300/5300
ASSIGNMENT 6
Fall 2010
Individual work.
Due: 3 pm, Friday October 22.
1. A coach must assign four swimmers to a 200meter medley relay team.
She can choose from ﬁve available swimmers, each of whom could swim
the 50meter leg in any one of the four strokes. The swimmers’ best
times in each stroke are listed below (in seconds).
Stroke
Barbara
Carol
Dianne
Elizabeth
Olympia
Breaststroke
45.4
42.8
36.1
43.2
36.7
Butterﬂy
34.3
36.6
29.5
39.9
33.4
Backstroke
39.7
37.4
33.9
36.8
39.0
Freestyle
31.2
33.1
29.4
31.6
32.5
The coach wants the fastest possible team. Explain how to formulate
her task as an assignment problem, and solve it, using the AMPL
model ﬁle
transp.mod
. Also upload your data ﬁle at this website.
2. Consider the linear programming problem
max
x
1

2
x
2
x
1

2
x
2
≤
4
x
1

2
x
2
≥ 
4
x
1
,
x
2
unrestricted in sign
.
According to the fundamental theorem of linear programming, this
problem should be infeasible, unbounded, or have an optimal solution.
(a) Show that this problem is feasible and bounded.
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