Math 121 - Systems of Inequalities and Linear Programming

Math 121 - Systems of Inequalities and Linear Programming -...

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SYSTEMS OF INEQUALITIES AND LINEAR PROGRAMMING (1) A system of inequalities is a set of inequalities with the same set of variables. The solution set to the system of inequalities is called the feasible set , and it contains all the points that make every inequality in the system true. If at least one of the inequalities fails to be satisfied by the point given, then that point is not in the feasible set. Example of a system of inequalities: 8 x + 3 y 24 2 x + 3 y 12 y 1 (4 , 1) is in the feasible set, but (2 , 3) is not because it fails to satisfy the second inequality in the system. (2) To graph the feasible set of a single inequality: (1) First graph the boundary line. If the inequality is strictly less than ( < ) or strictly greater than ( > ), then the points on the boundary line are not in the feasible set and should be drawn with a dotted line. If the inequality is either ” ” or ” ,” then the points in the boundary line are in the feaasible set so the boundary line should be drawn as a solid line. (2) Next, pick a ”test point” and see if the test point lies in your feasible set. If your boundary line does not pass through the origin, it is convenient to pick (0 , 0) as your test point. If your boundary line does pass through (0
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