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3.2 Linear Programming 3 Credits AS 91574

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I can plot linear inequalities I can find regions of intersection

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Inequalities and Regions x y Shade the region for which x + 2y ≥ 6 1. Draw the boundary line equation x + 2y = Choose a test point in one of the 2 regions to see whether or not it satisfies the inequality, then shade the required region. (2,4)(2,4) x 4 = 10 ≥ 6 Boundary line solid if inequality is either ≤ or ≥ x + 2y = 6 y = -½x + 3 Finding the region for a single inequality y intercept 3, gradient –½

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x y Shade the region for which 2x - y < Draw the boundary line equation 2x - y = Choose a test point in one of the 2 regions to see whether or not it satisfies the inequality then shade the required region. (3,1)(3,1) 2 x = 5 > -1 2x - y = -1 y = 2x + 1 Boundary line dotted if inequality is either Inequalities and Regions Finding the region for a single Inequality y intercept 1, gradient 2

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Inequalities and Regions Finding the region for two inequalities x y Shade and label with the letter R, the region for which y ≥ 1 and x > 2. Draw boundary line y = 1 lightly shade the region for which y ≥ 1 isn’t true. Draw boundary line x = 2 lightly shade the region for which x > 2 isn’t true R Identify the blank region that satisfies both inequalities and label. Boundary line solid since inequality is ≥ Boundary line dotted since inequality is >

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Inequalities and Regions Finding the region for two inequalities x y Shade and label with the letter R, the region for which x + y < -2 and x ≤ 1 Draw line x + y = -2 y = -x – 2 lightly shade the region for which x + y < -2 isn’t true Draw line x = 1 lightly shade the region for which x ≤ 1 isn’t true Identify the blank region that satisfies both inequalities and label. Boundary line dotted since inequality is < Boundary line solid since inequality is ≤ R The origin (0.0) makes a useful test point. y intercept -2 and gradient -1

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Inequalities and Regions Inequalities that enclose a region of the plane. x y Shade and label with the letter R, the region for which y ≥ -3 and x > 1 and 2x + y < 3 Draw line y = -3 lightly shade the region for which y ≥ -3 isn’t true. Draw line x = 1 lightly shade the region for which x > 1 isn’t true Draw line 2x + y = 3 y = -2x + 3 y intercept 3 and gradient - 2 lightly shade the region for which 2x + y < 3 isn’t true The origin (0.0) makes a useful test point. R Identify the overlapping region that satisfies all 3 inequalities and label.

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Inequalities and Regions Inequalities that enclose a region of the plane. x y Shade and label with the letter R, the region for which y ≥ -3, x > -2, y 2x - 3 and x + y < 2 Draw line y = -3 lightly shade the region for which y ≥ -3 isn’t true Draw line x = -2 lightly shade the region for which x > -2 isn’t true Draw line y = 2x – 3 lightly shade the region for which y 2x – 3 isn’t true The origin (0.0) makes a useful test point. y intercept -3 and gradient 2. R Draw line x + y = 2 y = -x + 2 y intercept 2, gradient 1 lightly shade the region x + y < 2 isn’t true Identify the Blank region that satisfies all 4 inequalities and label.

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State clearly you are shading the region that does not satisfy the inequality

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I can plot linear inequalities I can find regions of intersection Delta 3.01 page page 48

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