A semi-conductor manufacturing company aims to optimize its production output across m of their products, such as various chips and integrated circuits. Each products require specific quantities of n raw materials such as: Silicon, Gallium, Arsenic, Phosphorus, Boron etc. where n < m. They have to fully utilize a fixed amount of available raw materials and this imposes a constraint on the production levels. The relationship between the products and raw materials is represented by matrix A Rnm. The elements aij of A can be interpreted as follows: A unit of product j requires aij units of raw material i. Let vector x Rm represent the production quantity, that is xj represents the production quantity for the jth product