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In any simplex table, if corresponding to any negative $\Delta$ j, all elements of the column are negative or zero, the solution under the test is

1. degenerate solution
2. unbounded solution
3. alternative solution
4. non-existing solution

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ans will be option B) unbounded solution .

An unbounded solution of a linear programming problem is a situation where objective function is infinite. A linear programming problem is said to have unbounded solution if its solution can be made infinitely large without violating any of its constraints in the problem. Since there is no real applied problem which has infinite return, hence an unbounded solution always represents a problem that has been incorrectly formulated. Under the Simplex Method, an unbounded solution is indicated when there are no positive values of Replacement(or exchange ) Ratio i.e. Replacement ratio values are either infinite(when denominator has zero value) or negative(denominator is negative). In this case there is no outgoing variable.

by Boss (48.8k points)