1. Give the dual of each of the following linear programs: (a) maximize 100x₁+2002+300x3 + 400x4 subject to x+2x2+3x3 - 4x4 ≤10, -5x-6x2-7x3+8x4-20, 9x1 +102+11x3 - 12x4 = 30, 11, 130, 14 ≤0, 12 unrestricted

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Q: b) Consider the following linear program: Maximize: z=x. + 3x. + 2x. + 2x. subject to: x + 2x. + x,…

A: Given linear programming problem is where all variables are non- negative.

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Q: Maximize subject to: Z = $140×₁ + $150x₂ 8x1 + 2x₂ 40 9x2 + 3x₂ ≤ 120 X1, X₂ ≥0

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Q: Reformulate the problem to a linear program in canonical form (maximization): minimize 2x1 − |8x2 −…

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Q: 1. Give the dual of each of the following linear programs: (a) maximize 5x₁ + 8x₂ + x3 + 2x₁ subject…

A: Solution:Primal is  MAX Zx =   5 x1 + 8 x2 +   x3 + 2 x4 subject to   3 x1 + 3 x2…

Q: 3x, +3x, +2x; +1 MaxZ = 2x, +.x, +x; +1 S.t. 2.x, +5x, +x; < 2 X +2x, +3.x; < 3

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Q: Write the dual of the following linear program. maximize 3.x1 + 4x2 – 2x3 subject to Xi + x2 + x3 =…

A: We have to find the dual of the linear programming problem.

Q: Find the optimal Solution for the Following linear programming model using the graphical method :…

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Q: what's the dual problem of the following linear program: maximize 5x1 + 4x2 + 3x3 4x1 + 3x2 + x3 ≤…

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Q: what's the dual problem of the following linear program: minimize 10x1 + 8x2 + 5x3 2x1 + 3x2 + x3 ≥…

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Q: 15 X6 0. X3 X5 -5 01 15 1 -1 x M= 10 %3D 01 -1 0. 1 0. 10 0. -1 1. -1

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Q: Reformulate the problem to a linear program in canonical form (maximization): minimize 2x1 |8x2-3x3|…

A: we introduce three auxiliary variables to handle the absolute value term |8x2−3x3|: Let y1 represent…

Q: Solve the following linear program graphically: Maximize P = 4X1 + 6X2 Subject to X1+ X2 0

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Q: The region R is shaded in orange below. 1 -1 1 -2 What can you say about the sign of the following…

A: Ans is I is positive

Q: 1. Give the dual of each of the following linear programs: (a) maximize 5x₁ +8₂ +3 + 2x4 subject to…

A: Linear programming problem Advance maths

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Q: 1. Give the dual of each of the following linear programs: (a) 100x1200x2 + 300x3 + 400x4 maximize…

A: We have to find the dual of the primal problem.

Q: (b) maximize ᏆᎪ subject to x4x12x2+4x3, x42x13x2 - 5x3, x43x14x2+6x3, x1 + x2 x3 = 1, x1, x2, x30,…

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Q: Q.2// Give the dual programming from the mathematical model : Max Z = %3D 3x1 + 6x2 s.t. 4x1 + 5x2 <…

A: Here the given problem is                                           Max Z=3x1+6x2…

Q: So, what does "dynamic programming" really entail?

A: Dynamic programming is a mathematical optimization method and a computer programming method.

Q: Consider the following linear program: max z = -2x1 + x2 – 4x3 +3x4 subject to x1 + x2 + 3x3 + 2x4…

A:

Q: 2. Describe the solution set in R³ of the linear system - 1, x1 + 3x2 + 5x3 = 2x1 + x₂ + 5x3 = 3,…

A: Linear equations are  x1 + 3x2 + 5x3 = -1 2x1 + x2 + 5x3 = 3

Q: Consider the following linear program: Maximize: z= x +3x + 2x + 2x. subject to: x + 2x. +x + 3x.…

A: Given linear programming problem is  where all variables are non- negative.

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Q: Consider the following linear program: maximize subject to 3x1 + x2 + 4x3 21+3x2 + x3 ≤ 5 1 + 2x2 +…

A: The corresponding dual problem is    Minimize   5y1 + 7y2  subject to              y1 + y2 3…