I find the lack of pictures and/or equations in this article disappointing. There are much better explanations out there.

Linear programming didn't really "click" for me until I read Tim Roughgarden's notes:

* L7 (Intro): http://timroughgarden.org/w16/l/l7.pdf

* L8 (Duality I): http://timroughgarden.org/w16/l/l8.pdf

* L9 (Duality II: http://timroughgarden.org/w16/l/l9.pdf