![]() ![]() ![]() 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.
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