Solve this LP problem: 1. Maximize z = 20x₁ + 10x₂ + x3 Subject to: 3x₁ - 3x₂ + 5x3 ≤ 50 x₁ + x₂ ≤ 10 X₁-x₂ + 4x₂ ≤ 20 X₁, X₂, X3 ²0 Requirements: a) By inspecting the constraints, determine the direction (x₁, x₂, or x²) in which the solution space is unbounded. Support your answer. b) Verify using simplex calculation.

Q: 2. Maximize z = 2x₁ - 1x₂ + 3x3 Subject to: 1x₁ - 5x₂ + x₂ ≤ 10 - - 2x₁ − 1x₂ − 1x₂ + ≤ 40 X₁, X₂,…

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Q: Maximize z = 20x₁ + 10x₂ + x3 Subject to: 3x₁ - 3x₂ + 5x3 ≤ 50 x₁ + x₂ ≤ 10 X₁-x₂ + 4x₂ ≤ 20 X₁, X₂,…

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Q: a. Consider the following constraints: + 2x₂ ≤ 4 X1 -X₁ + X2 ≤ 1 X1, X2 ≥ 0. After adding the slack…

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Q: Maximize the function p = -x+y over the following constraints: a) x+y>=4, x>=0, y>=0, -x+2y<=2,…

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Q: B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂-x3 Subject to: x₁ + x₂ + 2x32 3…

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Q: Q2. Considering the following problem: Maximize Z = 50x₁ + 80x₂ subject to: X₁ + X₂ ≤ 20 5x₁ + 2x₂ ≤…

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Q: 8. min 3x1 + 4x2 + 6x3 +7x4+x5 2x1x2 + x3 + 6x4 5x5 6 x1 + x2 + 2x3 + x4 + 2x5 2 3 1, 2, 3, 4, 5 2 0…

A: given system min  3x1+4x2+6x3+7x4+x5         2x1-x2+x3+6x4-5x5≥6         x1+x2+2x3+x4+2x5≥3…

Q: 5. Consider the following problem Maximize Z = 2x₁2x₂ + 3x3, subject to -x₁ + x₂ + x3 ≤ 4 2x₁ - x₂ +…

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Q: Form the dual maximization problem (Use x,, Xa, and x, as the variables and fas the function.) and…

A: MIN g = 13y1 + 12y2subject toy1 + y2 &gt;= 1002y1 + y2 &gt;= 1406y1 + 5y2 &gt;= 580and y1,y2 &gt;=…

Q: C(0,6) b. x + 2y ≤ 10 3x + 4y ≤ 24 c. x+2y> 10 3x + 4y ≤ 24 (0,5) d. x + 2y ≤ 10 3x+4v > 24 B(4,3)…

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