A tourist wants to make a good trip at the weekend with his friends.

They will go to the mountains to see the wonders of nature.   So he needs some items during the trip.   Food, clothing, etc.   He has a good knapsack for carrying the things, but he knows that he can carry only 4 kg weight in his knapsack, because they will make the trip from morning to evening.

He creates a list of what he wants to bring for the trip, but the total weight of all items is too much.   He adds a value to each item.   The value represents how important the thing for the tourist.

The list contains which items are the wanted things for the trip, what is the weight and value of an item, and how many units does he have from each items.



This is the list:


 Table of potential knapsack items


 item 
 weight (dag) (each) 
 value (each) 
 piece(s)


 map 
 9 
 150 
 1


 compass 
 13 
 35 
 1


 water 
 153 
 200 
 2


 sandwich 
 50 
 60 
 2


 glucose 
 15 
 60 
 2


 tin 
 68 
 45 
 3


 banana 
 27 
 60 
 3


 apple 
 39 
 40 
 3


 cheese 
 23 
 30 
 1


 beer 
 52 
 10 
 3


 suntan cream 
 11 
 70 
 1


 camera 
 32 
 30 
 1


 T-shirt 
 24 
 15 
 2


 trousers 
 48 
 10 
 2


 umbrella 
 73 
 40 
 1


 waterproof trousers 
 42 
 70 
 1


 waterproof overclothes 
 43 
 75 
 1


 note-case 
 22 
 80 
 1


 sunglasses 
 7 
 20 
 1


 towel 
 18 
 12 
 2


 socks 
 4 
 50 
 1


 book 
 30 
 10 
 2


 knapsack 
 ≤400 dag 
 ? 
 ?



The tourist can choose to take any combination of items from the list, and some number of each item is available   (see the column   piece(s)   in the list above).

He may not cut the items, so he can only take whole units of any item.



Task

Show which items does the tourist carry in his knapsack so that their total weight does not exceed 4 kg, and their total value is maximized.



Related tasks

   Knapsack problem/Unbounded
   Knapsack problem/Continuous
   Knapsack problem/0-1


/*Knapsack
 
  This model finds the integer optimal packing of a knapsack
 
  Nigel_Galloway
  January 9th., 2012
*/
set Items;
param weight{t in Items};
param value{t in Items};
param quantity{t in Items};
 
var take{t in Items}, integer, >=0, <=quantity[t];
 
knap_weight : sum{t in Items} take[t] * weight[t] <= 400;
 
maximize knap_value: sum{t in Items} take[t] * value[t];
 
data;
 
param : Items          : weight   value   quantity :=
         map		  9	   150        1
         compass          13	   35	      1
         water		  153	   200        2
         sandwich	  50	   60	      2
         glucose	  15	   60	      2
         tin		  68	   45	      3
         banana		  27	   60	      3
         apple		  39	   40	      3
         cheese		  23	   30	      1
         beer		  52	   10	      3
         suntancream	  11	   70	      1
         camera		  32	   30	      1
         T-shirt	  24	   15	      2
         trousers	  48	   10	      2
         umbrella	  73	   40	      1
         w-trousers	  42	   70	      1
         w-overclothes	  43	   75	      1
         note-case	  22	   80	      1
         sunglasses	  7        20	      1
         towel		  18	   12	      2
         socks		  4        50	      1
         book		  30	   10	      2
;
 
end;