Linear Programming


Linear programming is a mathematical method used to solve resource allocation problems, which arise “whenever there are a number of activities to be performed, but limitations on either the amount of resources or the way they can be spent.” For example, it can be used to determine the best way to:

  • Distribute merchandise from a number of warehouses to a number of customers;
  • Assign personnel to various jobs;
  • Design shipping schedules;
  • Select the product mix in a factory to make the best use of machine and labor hours available while maximizing the firm’s profit;
  • Route production to optimize the use of machinery.

In order for managers to apply linear programming successfully, the problem must meet certain basic requirements: There must be a stated, quantifiable goal, such as “minimize total shipping costs”; the resources to be utilized must be known (a firm could produce 200 of one item and 300 of another, for instance, or 400 of one or 100 of another); all the necessary relationships must be expressed in the form of mathematical equations or inequalities; and all these relationships must be linear in nature.

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