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The problem of solving a system of linear inequalities dates back at least as far as Fourier when he used inequalities in Fourier transforms. The ability to sketch regions defined by linear inequalities is helpful when studying linear programming. Linear programming arose as a mathematical model developed during the Second World War to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. It was kept secret until 1947. Postwar, many industries found its use in their daily planning.

Joseph Fourier the French Mathematician was born on the 21st of March 1768. He was the son of a tailor, and was left an orphan in his eighth year; but, through the kindness of his friend, admission was gained into the military school .He soon distinguished himself as a student and made rapid progress, especially in mathematics.

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