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.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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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 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 + 6 y
subject to
x + 3y 2 5
2х + у2 3
x 2 0,
y > 0.
3.2 The Duality Theorem
183
7. Мaximize
8x, + 9x2 + 5x3
subject to
X1 + x2 + 2x3 < 2
2х, + 3x, + 4x; < 3
Зх, + 3х, + хз < 4
X; 2 0, j= 1,2,3
Transcribed Image Text: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 + 6 y subject to x + 3y 2 5 2х + у2 3 x 2 0, y > 0. 3.2 The Duality Theorem 183 7. Мaximize 8x, + 9x2 + 5x3 subject to X1 + x2 + 2x3 < 2 2х, + 3x, + 4x; < 3 Зх, + 3х, + хз < 4 X; 2 0, j= 1,2,3
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