Fall 2011 Math 141 Exam 2 Topics courtesy: Kendra Kilmer (covering Sections 3.1-3.3, 6.1-6.4, and 7.1) Section 3.1 • To graph a system of linear inequalities: • Solve all inequalities for y . • Graph the corresponding equations. If the inequal-ity is a strict inequality ( < or > ) draw the line as a dotted line to represent that the points on the line are NOT part of the solution. If the inequaility is inclusive ( ≤ or ≥ ) draw the line as a solid line to represent that the points on the line are part of the solution. • Determine which half-plane satisﬁes the inequality. You can do this by using a test point or by using the following “rules”. Please note that these “rules” only work once we have the inequality solved for y : • If you have y ≤ f ( x ) or y < f ( x ) the solution set lies below the line. • If you have y ≥ f ( x ) or y > f ( x ) the solution set lies above the line. • Our solution set (feasible region) consists of all points that satisfy all of the inequalities. • A solution set is bounded if all of the points in our solution set can be enclosed by a circle. Otherwise, we say that the solution set is
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