set ITEMS:=1..5;

param knapsack_size:=50;
param size{i in ITEMS};
param benefit{i in ITEMS};

set S{k in 1..5} := {j in ITEMS: size[j] > knapsack_size/k};

var copies{j in ITEMS} >=0;

maximize total_benefit: sum{j in ITEMS}benefit[j]*copies[j];

subject to size_constraint: sum{j in ITEMS}size[j]*copies[j]<=knapsack_size;

#s.t. cutplane{k in 1..5}: sum{j in S[k]}copies[j] <= k-1;


data;

param size:=
1	21
2	11
3	51
4	26
5	30;

param benefit:=
1	37
2	12
3	500
4	50
5	41;