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Ingy döt Net 2023-07-01 11:58:00 -04:00
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A thief burgles a butcher's shop, where he can select from some items.
The thief knows the weights and prices of each items.   Because he has a knapsack with 15 kg maximal capacity, he wants to select the items such that he would have his profit maximized.   He may cut the items;   the item has a reduced price after cutting that is proportional to the original price by the ratio of masses.   That means:   half of an item has half the price of the original.
This is the item list in the butcher's shop:
::::::{| style="text-align: left; width: 40%;" border="4" cellpadding="2" cellspacing="2"
|+ Table of potential knapsack items
|- style="background-color: rgb(255, 204, 255);"
! Item !! Weight (kg) !! Price (Value)
|-
| beef || 3.8 || 36
|-
| pork || 5.4 || 43
|-
| ham || 3.6 || 90
|-
| greaves || 2.4 || 45
|-
| flitch || 4.0 || 30
|-
| brawn || 2.5 || 56
|-
| welt || 3.7 || 67
|-
| salami || 3.0 || 95
|-
| sausage || 5.9 || 98
|- style="background-color: rgb(255, 204, 255);"
| Knapsack || <=15 kg || ?
|}
<br>
;Task:
Show which items the thief carries in his knapsack so that their total weight does not exceed 15 kg, and their total value is maximized.
;Related tasks:
* &nbsp; [[Knapsack problem/Bounded]]
* &nbsp; [[Knapsack problem/Unbounded]]
* &nbsp; [[Knapsack problem/0-1]]
<br><br>
;See also:
* &nbsp; Wikipedia article: &nbsp; [[wp:Continuous_knapsack_problem|continuous knapsack]].
<br><br>