**Problem definition:** Given a universe $U$ of $n$ elements, a collection of subsets of $U$, $S = {S_1,…, S_k}$, and a cost function $c: S to Q^{+}$. Find a minimum cost subcollection of $S$ that covers all elements of $U$.

**The provided algorithm (Approximation algorithms – Vijay V. Vazirani)**

**Part of the proof where I have trouble to understand**

**My question**

I have a difficult time to understand the last in equality, if $|bar{C}| leq n – k + 1$, why does $cfrac{OPT}{|bar{C}|} leq cfrac{OPT}{n – k + 1}$ hold?