solve the problem, set up and solve the dual problem, then check they satisfy the duality theorems. In Exercises 6 and 7, solve the given linear programming problem using thesimplex method. Also, set up and solve the dual of the given problem. Finally,verify that your solutions satisfy part (b) (iii) of the Duality Theorem.6. Minimizez = 4x + 6 ysubject tox + 3y 2 52х + у2 3x 2 0,y > 0.3.2 The Duality Theorem1837. Мaximize8x, + 9x2 + 5x3subject toX1 + x2 + 2x3 < 22х, + 3x, + 4x; < 3Зх, + 3х, + хз < 4X; 2 0, j= 1,2,3

“Since you have asked multiple question, we will solve the first question for you. If you want any…

Answered: In Exercises 6 and 7, solve the given…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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B. Direction. Find a counterexample for each of the following statements. Show your solution. Write your answer on the space provided. 1. For all integers x, x > 2. For all real numbers x, |x +3| = |x| + 3. 3. For all real numbers x, -x < x. 11
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Determine x and y in terms of b₁ and b2 if The result is x = In this case there is x + 2 y = b₁ - 2 x − 3 y=b₂. and y = a unique solution whatever b₁ and b2 are O a unique solution as long as b₁ and b2 satisfy some condition either zero solutions or an infinite family of solutions, depending on the values of b1 and b2.
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Consider the equations A) x² – 3x x² - 9 x² Which of the following statement is true? = 0 and B) x² – 3x 3x + 9 0. (a) the set of the solutions of A) is included in the set of the solutions of B) (b) the two equations have the same set of solutions (c) the equations A) and B) have two solutions in common (d) the set of the solutions of B) is included in the set of the solutions of A) X (e) the equations A) and B) do not have any common solution The correct answer is: the set of the solutions of A) is included in the set of the solutions of B)
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Consider the equations x² - 2x A) x² - 2x x³8 :0 and B) = 0. x³ +8 Which of the following statement is true? (a) the equations A) and B) do not have any common solution X (b) the set of the solutions of B) is included in the set of the solutions of A) (c) the set of the solutions of A) is included in the set of the solutions of B) (d) the two equations have the same set of solutions (e) the equations A) and B) have two solutions in common
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Q1) Solve the following linear equation by Grammar's rule. x + 2z = 1 y = -z - 1 x = -y +z+ 2

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In Exercises 6 and 7, solve the given linear programming problem using the simplex method. Also, set up and solve the dual of the given problem. Finally, verify that your solutions satisfy part (b) (iii) of the Duality Theorem. 6. Minimize z = 4x + 6y subject to x + 3y > 5 2х + y2 3 х2 0, у20.