14111cwir4ws.1 - • If you have y ≥ f x or y> f x the...

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c Kendra Kilmer September 27, 2011 Fall 2011 Week-in-Review #4 courtesy: Kendra Kilmer (covering Sections 3.1-3.3) Section 3.1 To graph a system of linear inequalities: Solve all inequalities for y . Graph the corresponding equations. If the inequality 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.
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Unformatted text preview: • 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 iequalities. • 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 unbounded . • A corner point is a point along the boundary of our feasible region in which we have a sharp turn. 1. Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all corner points. (a) x + y ≥ 5 x ≤ 10 y ≤ 8 x ≥ , y ≥ (b) 20 x + 10 y ≥ 100 10 x + 20 y ≥ 100 10 x + 10 y ≥ 80 x ≥ , y ≥ 1...
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