Can MONOTONE WSAT be in solved in polynomial time? In the weighted monotone satisfiability problem (MONOTONE WSAT), the input is an n-variable MONOTONE CNF Boolean formula (when there is no a clause with a negated variable) and an integer k, and the problem is to decide whether there exists a satisfying assignment in which at most k of the variables are true. Can MONOTONE WSAT be in solved in polynomial time or is also NP-complete?
This problem is indeed NP-complete.

Actually, the answer for this question is answered in: 

https://cs.stackexchange.com/questions/11558/prove-np-completeness-of-deciding-satisfiability-of-monotone-boolean-formula

Therefore, this question is closed and answered...