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Summer 2004
Practice Prelim 1
This is a practice prelim. Its goal is to give an
idea
of the kind of
problems that can be asked. It is by no mean a complete collection of all
the possible questions that can show up in the prelim.
1. For each of the following properties, write down a 2dim LP that satisﬁes the speciﬁed prop
erty (one LP per subproblem). Draw the feasible region of the LP’s (including the isoproﬁt
line). Each of your LP’s should have at most 2 functional constraints (plus nonnegativity
constraints, if you like):
(a) Every feasible point of the LP is also an optimal point though the feasible region is NOT
a point.
(b) The LP has a redundant constraint.
(c) The LP is infeasible.
2. For each of the following statements decide whether it is true or false. If you think it is true,
provide a brief explanation. If you think it is false, provide a counter example:
a. Every LP problem can be converted to an equivalent one in standard form.
b. In a feasible LP problem, the best CFP is always an optimal solution.
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 Fall '08
 TODD

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