linear programming simplex method example

The set of applications of linear programming is literally too long to list. It includes everything from production scheduling to web advertising optimization to clothing manufacturing. LP touches nearly every commercial industry in some way. Using linear algebra notation, a linear program can be described as follows: Objective: minimize c Tx Constraints: A x = b (linear constraints) l ≤ x ≤ u (bound constraints) When described in this form, the vector x represents the decision variables, the vector c captures the linear objective function, the matrix equation Ax = b specifies the linear constraints on x, and the vectors l and u give the lower and upper bounds on x. The LP model would have a set of decision variables that capture the amount of each food to buy, a linear objective that minimizes the total cost of purchasing the chosen foods, and a linear constraint for each nutrient, requiring that the chosen foods together contain a sufficient quantity of that nutrient. Linear programming (LP) is a powerful framework for describing and solving optimization problems. It allows you to specify a set of decision variables, and a linear objective and a set of linear constraints on these variables. To give a simple and widely used example, consider the problem of minimizing the cost of a selection of foods that meets all the recommended daily nutrient guidelines. Note, you can also see a list of code examples, across a range of programming languages on our linear programming code examples page.

Linear programming simplex method example