Question

Suppose the following tableau was obtained in the course of solving a linear program with non-negative variables X1, X2, X3 and two inequalities. The objective function is maximized and slack variables sy and sq were added. 2 21 0 0 81 0 RHS 82 1 22 23 a b -2 2 - 1 3 82 4 3 -5 c 0 0 0 3 Give conditions on a, b and cthat are required for the following statements to be true: The current basic solution is a feasible basic solution. For parts.() through (iv), assume that the condition found in.(1).still holds (ii) The current basic solution is optimal. (iii) The linear program is unbounded, (iv) The current basic solution is optimal and there are alternate optimal solutions.

Answer 1

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i)

c> 0 ... a and b can be anything

ii)

a>0 , b >0

iii) a<0 , b can be anything

iv)

a>0 and b = 0