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3.2 Linear Programming 3 Credits AS 91574

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**Linear Programming I can plot linear inequalities**

Learning objectives I can plot linear inequalities I can find regions of intersection

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**Inequalities and Regions**

Finding the region for a single inequality Shade the region for which x + 2y ≥ 6 x y 1 2 3 4 5 -1 -2 -3 -4 -5 (2,4) 2 + 2 x 4 = 10 ≥ 6 Boundary line solid if inequality is either ≤ or ≥ 1. Draw the boundary line equation x + 2y = 6. x + 2y = 6 y = -½x + 3 y intercept 3, gradient –½ 2. Choose a test point in one of the 2 regions to see whether or not it satisfies the inequality, then shade the required region.

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**Inequalities and Regions**

Finding the region for a single Inequality x y 1 2 3 4 5 -1 -2 -3 -4 -5 Shade the region for which 2x - y < -1 2 x = 5 > -1 1. Draw the boundary line equation 2x - y = -1 Boundary line dotted if inequality is either < or > (3,1) 2x - y = -1 y = 2x + 1 y intercept 1, gradient 2 2. Choose a test point in one of the 2 regions to see whether or not it satisfies the inequality then shade the required region.

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**Inequalities and Regions**

Finding the region for two inequalities x y 1 2 3 4 5 -1 -2 -3 -4 -5 Shade and label with the letter R, the region for which y ≥ 1 and x > 2. R Draw boundary line y = 1 lightly shade the region for which y ≥ 1 isn’t true. Boundary line solid since inequality is ≥ Draw boundary line x = 2 lightly shade the region for which x > 2 isn’t true Boundary line dotted since inequality is > Identify the blank region that satisfies both inequalities and label.

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**R Inequalities and Regions Finding the region for two inequalities y**

x y 1 2 3 4 5 -1 -2 -3 -4 -5 Shade and label with the letter R, the region for which x + y < -2 and x ≤ 1 Boundary line dotted since inequality is < Boundary line solid since inequality is ≤ Draw line x + y = -2 y = -x – 2 y intercept -2 and gradient -1 lightly shade the region for which x + y < -2 isn’t true The origin (0.0) makes a useful test point. Draw line x = 1 lightly shade the region for which x ≤ 1 isn’t true R Identify the blank region that satisfies both inequalities and label.

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**R Inequalities and Regions**

Inequalities that enclose a region of the plane. x y 1 2 3 4 5 -1 -2 -3 -4 -5 Shade and label with the letter R, the region for which y ≥ -3 and x > 1 and 2x + y < 3 Identify the overlapping region that satisfies all 3 inequalities and label. The origin (0.0) makes a useful test point. Draw line y = -3 lightly shade the region for which y ≥ -3 isn’t true. Draw line x = 1 R lightly shade the region for which x > 1 isn’t true Draw line 2x + y = 3 y = -2x + 3 lightly shade the region for which 2x + y < 3 isn’t true y intercept 3 and gradient - 2

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**R Inequalities and Regions**

Inequalities that enclose a region of the plane. x y 1 2 3 4 5 -1 -2 -3 -4 -5 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 Draw line x + y = 2 y = -x + 2 The origin (0.0) makes a useful test point. The origin (0.0) makes a useful test point. lightly shade the region for which y ≥ -3 isn’t true y intercept 2, gradient 1 lightly shade the region x + y < 2 isn’t true Draw line x = -2 lightly shade the region for which x > -2 isn’t true R Identify the Blank region that satisfies all 4 inequalities and label. Draw line y = 2x – 3 y intercept -3 and gradient 2. lightly shade the region for which y 2x – 3 isn’t true

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

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**Success Criteria I can plot linear inequalities**

I can find regions of intersection Delta 3.01 page 47 3.02 page 48

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