examp Example 1.16 : Minimize Z= 4x + X2 Subject to on is 3x1 + x2 = 3 4x1 + 3x2 2 6 X1 + 2x2 = 4; X1, X2 > 0. by using simplex method
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Step-by-step explanation:
Given that 5x1 + x2 ≥ 10 Let 5x1 + x2 = 10 x1 0 2 x2 10 0 Also given that x1 + x2 ≥ 6 Let x1 + x2 = 6 x1 0 6 x2 6 0 Also given that x1 + 4x2 ≥ 12 Let x1 + 4x2 = 12 x1 0 12 x2 3 0 To get C 5x1 + x2 = 10 … (1) x1 + x2 = 6 … (2) (1) – (2) ⇒ 4x1 = 4 ⇒ x1 = 1 x = 1 substitute in (2) ⇒ x1 + x2 = 6 ⇒ 1 + x2 = 6 ⇒ x2 = 5 ∴ C is (1, 5) To get B x1 + x2 = 6 x1 + 4x2 = 12 (1) – (2) ⇒ -3x2 = -6 x2 = 2 x2 = 2 substitute in (1), x1 = 4 ∴ B is (4, 2) The feasible region satisfying all the conditions is ABCD. The co-ordinates of the comer points are A(12, 0), B(4, 2), C(1, 5) and D(0, 10). The minimum value of Z occours at C(1, 5). ∴ The optimal solution is x1 = 1, x2 = 5 and Zmin = 13Read more on Sarthaks.com - https://www.sarthaks.com/987153/minimize-z-3x1-2x2-subject-to-the-constraints-5x1-x2-10-x1-x2-6-x1-4x2-12-and-x1-x2-0