Consider the equality integer knapsack problem: (P). min 5 7 2 5 5 19 8 {...

 

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Consider the equality integer knapsack problem: (P₁). min 5 7 2 5 5 19 8 {£ cx = ²x − ³x + ³x - 2x + ²x = xez}} : -X₁ 4 ·X3 X5 12 6 j=1 (i) Show that the problem (P₂) 7 1 min { £95 : ¾ x + 3x + 2 x + ² x + £ x = 3 + 1, w, 12 j=1 x = Z³, w€ Z¹ '+' EZ:} + is a relaxation of P₁. (ii) Show that the problem 5 3 7 { Σ9x : 2x + 3x + 1/x + 1⁄2 x + √x ≥ 3.X ER! } > + j=1 is a relaxation of P₂. (P3) min Consider the equality integer knapsack problem: (P₁). min 5 7 2 5 5 19 8 {£ cx = ²x − ³x + ³x - 2x + ²x = xez}} : -X₁ 4 ·X3 X5 12 6 j=1 (i) Show that the problem (P₂) 7 1 min { £95 : ¾ x + 3x + 2 x + ² x + £ x = 3 + 1, w, 12 j=1 x = Z³, w€ Z¹ '+' EZ:} + is a relaxation of P₁. (ii) Show that the problem 5 3 7 { Σ9x : 2x + 3x + 1/x + 1⁄2 x + √x ≥ 3.X ER! } > + j=1 is a relaxation of P₂. (P3) min

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Sob 4 1212 PUP 3 212235 12 16 ... View the full answer