Continuous backpack with multiple choice items is the problem where you need to collect items by one from each of distinct sets and associate them with rational numbers so that their sum of weights will not be greater than K and sum of costs will not be less than B.


*Computers and Intractability: A Guide to the Theory of NP-Completeness By Michael R. Garey, David S. Johnson* is saying that the np-hard partition problem (where you need to choose items from a set so that the sum of the function values on these items is equal to the sum of the function values on other items) can be reduced to this problem.


But how to reduce it?



Continuous backpack with multiple choice items. NP prove
I have found the prove of NP-completeness at <http://www.orsj.or.jp/~archive/pdf/e_mag/Vol.23_01_028.pdf> P. 30-32


