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Ingy döt Net 2013-04-11 12:07:39 -07:00
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See also: [[Knapsack problem]] and [[wp:Continuous_knapsack_problem|Wikipedia]].
A robber burgles a butcher's shop, where he can select from some items. He 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:
{| style="text-align: left; width: 80%;" 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 || ?
|}
'''Which items does the robber carry in his knapsack so that their total weight does not exceed 15 kg, and their total value is maximised?'''