Question: 5. Consider the equality integer knapsack problem: 7 5 (P1). min{c;t;: 2 3+2 + z 23 5 19 8 *4 + 25 = 12 6

5. Consider the equality integer knapsack problem: 7 5 (P1). min{c;t;:

5. Consider the equality integer knapsack problem: 7 5 (P1). min{c;t;: 2 3+2 + z 23 5 19 8 *4 + 25 = 12 6 j=1 (i) Show that the problem 5 3 1 1 7 1 2 (P2) min{{cj;: x2+372+273 +izatot5 = +w, x Z, we Z}} ; !! j=1 is a relaxation of Pi. (ii) Show that the problem 5 (P3) min{cja; : *1 +32 +353 +1264 +5 2 tery} j=1 is a relaxation of P2. 5. Consider the equality integer knapsack problem: 7 5 (P1). min{c;t;: 2 3+2 + z 23 5 19 8 *4 + 25 = 12 6 j=1 (i) Show that the problem 5 3 1 1 7 1 2 (P2) min{{cj;: x2+372+273 +izatot5 = +w, x Z, we Z}} ; !! j=1 is a relaxation of Pi. (ii) Show that the problem 5 (P3) min{cja; : *1 +32 +353 +1264 +5 2 tery} j=1 is a relaxation of P2

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