5.6 - Linear Programming

5.6 - Linear Programming - <?xml version="1.0"...

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<?xml version="1.0" encoding="iso-8859-1"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>5.6 - Linear Programming</title> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> <style type="text/css"> <!-- td { text-align: center; vertical-align: top; padding-right: 1em; padding-left: 1em; } .solution { background-color: #99FFCC; font-weight: bold; } --> </style> </head> <body> <h1>5.6 - Linear Programming</h1> <p>In business, it is often desirable to find the production levels that will produce the maximum profit or the minimum cost. The production process can often be described with a set of linear inequalities called constraints. The profit or cost function to be maximized or minimized is called the objective function. The process of finding the optimal levels with the system of linear inequalities is called linear programming (as opposed to non-linear programming).</p> <h2>Definitions</h2> <dl> <dt>Objective Function</dt> <dd>The linear function (equal sign) representing cost, profit, or some other quantity to be maximized of minimized subject to the constraints.</dd> <dt>Constraints</dt> <dd>A system of linear inequalities.</dd> <dt>Problem Constraints</dt> <dd>The linear inequalities that are derived from the application. For example, there may be only 40 hours a machine can be used in a week, so the total time it is used would have to be &lt;= 40. The problem constraints are usually stated in the story problem.</dd> <dt>Non-Negativity Constraints</dt> <dd>The linear inequalities x>=0 and y>=0. These are included because
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5.6 - Linear Programming - &lt;?xml version=&quot;1.0&quot;...

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