Consider the linear program maximize c1 + C%+...+ C subject to a11 + 922+...+ ainIn ...

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Consider the linear program maximize c₁1 + C₂%₂+...+ C₂²₂ subject to a11 + 9₁22+...+ ainIn ≤ ai b₁1₁+b₁2₂+...+binn = Bi ie [r] where r and s are positive integers. Further, consider the inequality obtained as follows: i=1 r Σ(₂1 +9;27₂+...+ ain£n ≤ai) + Σdi (b₁12₁ + b₁2æ2 + ... +bin£n = Bi) i=1 where % € R₂0 for all i € [s] and d; R for all i € [r]. Explain why adding this inequality to the linear program does not change the feasible region of the linear program. Consider the linear program maximize c₁1 + C₂%₂+...+ C₂²₂ subject to a11 + 9₁22+...+ ainIn ≤ ai b₁1₁+b₁2₂+...+binn = Bi ie [r] where r and s are positive integers. Further, consider the inequality obtained as follows: i=1 r Σ(₂1 +9;27₂+...+ ain£n ≤ai) + Σdi (b₁12₁ + b₁2æ2 + ... +bin£n = Bi) i=1 where % € R₂0 for all i € [s] and d; R for all i € [r]. Explain why adding this inequality to the linear program does not change the feasible region of the linear program.

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The given linear program is maximize c1x1 c2x2 cnxn subject to ai1x1 ai2x2 ainxn i for i in s bi1x1 bi2x2 binxn i for i in r where r and s are positiv... View the full answer