Introduction to Linear Programming

Suppose you manage a firm to produce m goods. These goods can be produced by n activities at varying levels x1, x2, ..., xn. One unit of activity j generates the amount aij of product i. Activity j has unit cost cj . Then ∑n j=1 aijxj units of goods i are produced. If you want to produce goods of amounts b1, b2, ..., bm, there are conditions ∑n j=1 aijxj ≥ bi, i = 1, 2, ...,m. You want to minimize the cost ∑n j=1 cjxj to produce the goods, then you have the following problem to solve,