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: 50%;" 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 || ? |}
;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: *   [[Knapsack problem/Bounded]] *   [[Knapsack problem/Unbounded]] *   [[Knapsack problem/0-1]]

;See also: *   Wikipedia article:   [[wp:Continuous_knapsack_problem|continuous knapsack]].