LP problem
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Suppose that we are trying to solve the following LP problem:
Maximize cTx, subject to
Ax <= b,
x >= 0.
Let A = (aij) be an m x n matrix. Suppose that, for some value of i, ai;j >= 0 for all
1 <= j <= n, and bi < 0 (bi is the i'th component of b). Prove that the LP problem is
infeasible.
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Solution Summary
LP problem is solved for maximization.
Solution Preview
Well, just write down what it means if ai:j >= 0 for some i. If you fix i and look at the ai:j for all possible j, you get the i th row of matrix A. Indeed, if, say, i=1, then the elements a11, a12, a13,..., a1n form the first row of A.
If, say, i=3, then the elements a31, a32, a33, ...
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