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Unformatted text preview: x for the problem and a vector d R n such that Ad , d and c T d > then the problem is unbounded. Exercise 3. Consider the linear program max { c T x : Ax = 0 ,x } , where A R m n and c R n . Prove that if x = 0 is not an optimal solution then the linear program is unbounded. Exercise 4. Consider the problem max { x : x < 1 } . Explain why the problem is not a linear program and show that it is not infeasible, not unbounded and has no optimal solution. Exercise 5. Convert the following linear program into standard equality form: min 7 x 13 x 3 x 1 + x 2 = 22 x 1 + x 24 x 3 1 2 x 2 + x 3 7 x 2 ,x 3 Exercise 6. Let A R m n , b R m and c R n . Convert the problem max { c T x : Ax b } into standard equality form. 1...
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 Fall '07
 S.Furino,B.Guenin

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