Given an algorithm for the Knapsack problem, can you also solve the min set covering problem? Min set covering problem: Knapsack problem:
max \sum_j c_j y_j such that ================================ Answer (As per Sune's recommendation below): rewriting and rearranging these constraints yields: This problem is indeed the desired knapsack problem. the " sum_j c_j" term in the objective is a constant and can therefore be ignored. After solving this knapsack problem, one can obtain a feasible solution to the set cover problem by setting y_j=1z_j. asked 11 Mar '15, 17:29 Joris Kinable 
Try to just substitute \(y_i=1z_i\) in the original problem and remember that \(\max f(x)=\minf(x)\) answered 11 Mar '15, 18:36 Sune Thanks, that indeed is correct. I've updated my question with the answer.
(11 Mar '15, 20:42)
Joris Kinable

You have a binary set covering problem with only one cover constraint?
@Joris Your definition of Set Cover is nonstandard. Here is the standard one.
@Austin: you are right. I'm not sure ow to name a problem having such a "cover" constraint. Yet I encounter these fairly frequently. Are you aware of a different name?