Min weight positive 3SAT.

Let us have a set of clauses of type (x or y or z) which always contain a disjunction of at most three variables and never contain negation. Next, let's have a function that assigns an integer weight to each variable. The aim is to find a subset of variables with the smallest possible sum of weights such that that setting these variables to 1 will fulfill all clauses. This problem is NP-complete, but there is an approximation algorithm with a constant approximation ratio. Find such an algorithm and prove that it has the required properties. Focus on the fact that there are no negations in the assignment. And no, there are no other variants of SAT.