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Question 1. Consider the following LP problem: min ACR s.t 2= 2x₁ +5x₂ 2 5, 9, -4, 0. A VIII -2x₁ + x₂ = x1, x₂ 2 min z = 2x₁ + 5x₂ s.t x1 <-X3 S Convert it into standard form. Check ift = (4.) is a feasible solution. If it is, then construct one feasible solution of the standard form from this solution. Solution: We only need to add a surplus variable, for the first constraint, and a slack variable, for the second constraint. -2x₁ + x₂ X.X.X.20 + x₁ = We can check thatx = (4.) is not a feasible solution of this problem since it does not satisfy the constraint -2x1 + x2 = -4.

Question 1. Consider the following LP problem: min ACR s.t 2= 2x₁ +5x₂ 2 5, 9, -4, 0. A VIII -2x₁ + x₂ = x1, x₂ 2 min z = 2x₁ + 5x₂ s.t x1 <-X3 S Convert it into standard form. Check ift = (4.) is a feasible solution. If it is, then construct one feasible solution of the standard form from this solution. Solution: We only need to add a surplus variable, for the first constraint, and a slack variable, for the second constraint. -2x₁ + x₂ X.X.X.20 + x₁ = We can check thatx = (4.) is not a feasible solution of this problem since it does not satisfy the constraint -2x1 + x2 = -4.

Advanced Engineering Mathematics
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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Question 1. Consider the following LP problem: min AER s.t 2= 2x₁ + 5x₂ X₁ 2 x₁ + x₂ s -2x₁ + x₂ = Convert it into standard form. Check ift (,) is a feasible solution. If it is, then construct one feasible solution of the standard form from this solution. Solution: We only need to add a surplus variable, for the first constraint, and a slack variable, for the second constraint. min z = 2x₁ + 5x₂ s.t - X3 x1 + x₂ -2x₁ + x₂ X1 X₂ X3 X4 20 +XA 5. 9, -4. 0. = 5 9 -4 We can check that = (4.) is not a feasible solution of this problem since it does not satisfy the constraint -2x1 + x2 = -4.
Transcribed Image Text:Question 1. Consider the following LP problem: min AER s.t 2= 2x₁ + 5x₂ X₁ 2 x₁ + x₂ s -2x₁ + x₂ = Convert it into standard form. Check ift (,) is a feasible solution. If it is, then construct one feasible solution of the standard form from this solution. Solution: We only need to add a surplus variable, for the first constraint, and a slack variable, for the second constraint. min z = 2x₁ + 5x₂ s.t - X3 x1 + x₂ -2x₁ + x₂ X1 X₂ X3 X4 20 +XA 5. 9, -4. 0. = 5 9 -4 We can check that = (4.) is not a feasible solution of this problem since it does not satisfy the constraint -2x1 + x2 = -4.
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