**Exercise 4.5**Let $\{d_1, \ldots, d_k\}$ be directions of unboundedness for the constraints:\[ Ax = b, \quad x \geq 0. \]Prove that \[ d = \sum_{i=1}^{k} \alpha_i d_i \quad \text{with} \quad \alpha_i \geq 0 \]is also a direction of unboundedness for these constraints.

A direction d is said to be direction of unboundedness for a LPP whose constraints is Ax=b, x≥0 if…

Answered: Let { d1, . . , di } be directions of…

Advanced Engineering Mathematics

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Author:Erwin Kreyszig

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Let { d1, . . , di } be directions of unboundedness for the constraints Ax = b, x > 0. Prove that k d = ) `a;d; with a; > 0 i=1 Is also a direction of unboundedness for these constraints.