Math 121 - Systems of Inequalities and Linear Programming

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

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Unformatted text preview: 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...
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Math 121 - Systems of Inequalities and Linear Programming -...

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