Unformatted text preview: ˆ 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
 Linear Algebra, Operations Research, Linear Programming, Optimization, linear program

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