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3.2 Linear Programming

3.2 Linear Programming. 3 Credits AS 91574. Linear Programming. Learning objectives. I can plot linear inequalities I can find regions of intersection. y. 5. ( 2 , 4 ). 4. 3. Boundary line solid if inequality is either ≤ or ≥. 2. 1. x. -4. -3. 2. 0. 1. 3. 4. -2. -1. 5.

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3.2 Linear Programming

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  1. 3.2 Linear Programming 3 Credits AS 91574

  2. Linear Programming Learning objectives • I can plot linear inequalities • Ican find regions of intersection

  3. y 5 (2,4) 4 3 Boundary line solid if inequality is either ≤ or ≥ 2 1 x -4 -3 2 0 1 3 4 -2 -1 5 -1 -2 -3 -4 -5 Inequalities and Regions Finding the region for a single inequality Shade the region for which x + 2y ≥ 6 2 + 2 x 4 = 10 ≥ 6  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.

  4. Inequalities and Regions Finding the region for a single Inequality y 5 (3,1) 4 3 Boundary line dotted if inequality is either < or > 2 1 x -4 -3 2 0 1 3 4 -2 -1 5 -1 -2 -3 -4 -5 Shade the region for which 2x - y < -1 2 x 3 - 1 = 5 > -1  1. Draw the boundary line equation 2x - y = -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.

  5. y 5 4 3 2 1 x -4 -3 2 0 1 3 4 -2 -1 5 -1 Boundary line solid since inequality is ≥ -2 -3 Boundary line dotted since inequality is > -4 -5 Inequalities and Regions Finding the region for two inequalities Shade and label with the letter R, the region for which y ≥ 1andx > 2. R 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 Identify the blank regionthat satisfies both inequalities and label.

  6. Inequalities and Regions Finding the region for two inequalities y 5 4 Boundary line dotted since inequality is < Boundary line solid since inequality is ≤ 3 2 1 x -4 -3 2 0 1 3 4 -2 -1 5 -1 The origin (0.0) makes a useful test point. -2 -3 -4 -5 Shade and label with the letter R, the region for which x + y < -2andx ≤ 1 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 Draw line x = 1 lightly shade the region for which x ≤ 1 isn’t true R Identify the blank regionthat satisfies both inequalities and label.

  7. y 5 4 3 The origin (0.0) makes a useful test point. 2 1 x -4 -3 2 0 1 3 4 -2 -1 5 -1 -2 -3 -4 -5 Inequalities and Regions Inequalities that enclose a region of the plane. Shade and label with the letter R, the region for which y ≥ -3andx > 1and2x + y < 3 Identify the overlapping region that satisfies all 3 inequalities and label. 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

  8. Inequalities and Regions Inequalities that enclose a region of the plane. y 5 4 3 The origin (0.0) makes a useful test point. The origin (0.0) makes a useful test point. 2 1 x -4 -3 2 0 1 3 4 -2 -1 5 -1 -2 -3 -4 -5 Shade and label with the letter R, the region for which y ≥ -3, x > -2, y  2x - 3andx + y < 2 Draw line y = -3 Draw line x + y = 2  y = -x + 2 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 regionthat 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

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

  10. Success Criteria • I can plot linear inequalities • Ican find regions of intersection Delta 3.01 page 47 3.02 page 48

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