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Unformatted text preview: x 1 ,x 2 and two constraints, is solved by introducing slack variables u 1 ,u 2 for the respective constraints. The ﬁnal tableau is x 1 x 2 u 1 u 2 x 1 1 21 16 x 2 11 3 12 1 2 28 The original right sides were 60 and 40 for the ﬁrst and the second constraint, respectively. If the original problem is modiﬁed by changing the 60 to 75, will optimality still occur with the same variables being basic? Justify your answer. Solution . Δ b 1 = 7560 = 15, and the new values of x 1 and x 2 in a basic solution are • x 1 x 2 ‚ = • 16 12 ‚ + 15 · • 21 ‚ = • 463 ‚ . Therefore, the basic solution to the modiﬁed problem with x 1 and x 2 being basic is not feasible. Optimality cannot occur with x 1 and x 2 being basic. 2...
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 Spring '08
 VOGELIUS
 Harshad number, optimality

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