**KNAPSACK:** Given a finite set *U*, a ``size''
and a ``value''
for each , a size constraint
, and a value goal
, is there a subset
such that
and
?

This can be seen as a knapsack, which has a size limit for the objects, as in the picture below.

The goal is to pick a collection of objects that will fit in the knapsack
and whose total value is at least *K* (*K* is input)

KNAPSACK =
subset *U*' of *U* such that
the sum of *s* values is at most *B*, and the sum of *v* values is at least
*K*}

Knapsack Problem Variant

Applet courtesy of the tutOR project,

Department of Mathematics and Statistics

University of Melbourne

Applet courtesy of the tutOR project,

Department of Mathematics and Statistics

University of Melbourne