Its been really long since I made a post, all these day's I'm doing a lot of theory and trying to come up with approximation algorithms to the Border Length Minimization Problem. After a long time I did prove the problem is NP-hard by reducing the T.S.P problem to the B.L.M.P problem. I'm now trying to find some approximation algorithms for the problem. I thought if I could strengthen my skills on inequalities it would be really great and I found a great problem book for inequalities by Michael Steele which has a good collections of problems on inequalities. In this post I provide my solutions to some of the problems which seemed interesting.