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Ex 12.1, 6 - Minimise Z = x + 2y. Show minimum Z occurs at

Ex 12.1, 6 - Chapter 12 Class 12 Linear Programming - Part 2
Ex 12.1, 6 - Chapter 12 Class 12 Linear Programming - Part 3 Ex 12.1, 6 - Chapter 12 Class 12 Linear Programming - Part 4


Transcript

Ex 12.1, 6 Solve the following Linear Programming Problems graphically: Minimise Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0. Show that the minimum of Z occurs at more than two points. Minimize Z = x + 2y Subject to 2x + y ≥ 3 x + 2y ≥ 6 x , y ≥ 0 Since, the region that is feasible is unbounded, Hence 6 may or may not be the minimum value of z We need to graph inequaality : There is no common point between feasible region & inequality ∴ Z = 6 is minimum on all points joining line (0, 3), (6, 0) i.e. Z = 6 will be minimum on x + 2y = 6 Explanation – Taking points on line x +2y = 6 Hence, Z is minimum at all the points joining (0, 3) & (6, 0) ⇒ Z will be minimum on all points joining line (0, 3) & (6, 0) ∴ Z will be minimum on x + 2y = 6

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.