Download presentation

Presentation is loading. Please wait.

Published byEsmeralda Towe Modified over 2 years ago

2
3.2 Linear Programming 3 Credits AS 91574

3
I can plot linear inequalities I can find regions of intersection

4
Inequalities and Regions x y 0 1 2 34 5 -2 -3-4 1 2 3 4 5 -2 -3 -4 -5 Shade the region for which x + 2y ≥ 6 1. Draw the boundary line equation x + 2y = 6. 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. (2,4)(2,4) 2 + 2 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

5
x y 0 1 2 34 5 -2 -3-4 1 2 3 4 5 -2 -3 -4 -5 Shade the region for which 2x - y < -1 1. Draw the boundary line equation 2x - y = -1 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. (3,1)(3,1) 2 x 3 - 1 = 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

6
Inequalities and Regions Finding the region for two inequalities x y 0 1 2 34 5 -2 -3-4 1 2 3 4 5 -2 -3 -4 -5 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 >

7
Inequalities and Regions Finding the region for two inequalities x y 0 1 2 34 5 -2 -3-4 1 2 3 4 5 -2 -3 -4 -5 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

8
Inequalities and Regions Inequalities that enclose a region of the plane. x y 0 1 2 34 5 -2 -3-4 1 2 3 4 5 -2 -3 -4 -5 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.

9
Inequalities and Regions Inequalities that enclose a region of the plane. x y 0 1 2 34 5 -2 -3-4 1 2 3 4 5 -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 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.

10
State clearly you are shading the region that does not satisfy the inequality

11
I can plot linear inequalities I can find regions of intersection Delta 3.01 page 47 3.02 page 48

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google