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1. Say whether or not each of the following is a linear program. If it is a linear program, then reformulate it in standard inequality form, giving the values of the vectors c and b, and the matrix A. If it is not a linear program, write a sentence or two explaining why. Note: to make your answers easier to mark, please order your vector of vari- ables by subscript. If 2 variables have the same subscript (because you have split a variable x; into x and x) list x first followed by x. For example: x¹ = (x1, T2, x3, x,x, x5) is ordered as described. (a) (b) (c) minimize subject to maximize subject to 5x1 + 6x3 2.9x1 + 6x2 +8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x118x₂ ≤ 14, X1, X2, X3 20 5x₁(1-3x2 + x3) - x2 X2 x₁ + 3x2 + x3 ≥ 4, -X₁ + X₂ X3 ≤ 3, -2x1 + x₂ <7, X1, X2, X3 20 maximize 2x1 + x2-3 subject to 4x₁ + x2 + 3x3 ≤ 1, -2x₂ + x3 ≤ 1, 4x2+2x3 = -7, ₁ unrestricted, x₂ ≤ 0, X3 20

1. Say whether or not each of the following is a linear program. If it is a linear program, then reformulate it in standard inequality form, giving the values of the vectors c and b, and the matrix A. If it is not a linear program, write a sentence or two explaining why. Note: to make your answers easier to mark, please order your vector of vari- ables by subscript. If 2 variables have the same subscript (because you have split a variable x; into x and x) list x first followed by x. For example: x¹ = (x1, T2, x3, x,x, x5) is ordered as described. (a) (b) (c) minimize subject to maximize subject to 5x1 + 6x3 2.9x1 + 6x2 +8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x118x₂ ≤ 14, X1, X2, X3 20 5x₁(1-3x2 + x3) - x2 X2 x₁ + 3x2 + x3 ≥ 4, -X₁ + X₂ X3 ≤ 3, -2x1 + x₂ <7, X1, X2, X3 20 maximize 2x1 + x2-3 subject to 4x₁ + x2 + 3x3 ≤ 1, -2x₂ + x3 ≤ 1, 4x2+2x3 = -7, ₁ unrestricted, x₂ ≤ 0, X3 20

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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1. Say whether or not each of the following is a linear program. If it is a linear program, then reformulate it in standard inequality form, giving the values of the vectors c and b, and the matrix A. If it is not a linear program, write a sentence or two explaining why. Note: to make your answers easier to mark, please order your vector of vari- ables by subscript. If 2 variables have the same subscript (because you have split a variable x; into x and x) list x first followed by x. For example: x¹ = (x1, T2, x3, x,x, x5) is ordered as described. (a) (b) (c) minimize 5x1 + 6x3 subject to 2.9x1 + 6x2 + 8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x₁18x2 ≤ 14, X1, X2, X3 20 maximize subject to 5x₁(1 − 3x₂ + x3) - X₂ x₁ + 3x2 + x3 ≥ 4, -X₁ + X₂ X3 ≤ 3, -2x1 + x₂ ≤ 7, X1, X2, X3 20 maximize 2x1 + x2x3 subject to 4x₁ + x₂ + 3x3 ≤ 1, -2x₂ + x3 ≤ 1, 4x2 + 2x3 = -7, ₁ unrestricted, X₂ ≤ 0, X3 20
Transcribed Image Text:1. Say whether or not each of the following is a linear program. If it is a linear program, then reformulate it in standard inequality form, giving the values of the vectors c and b, and the matrix A. If it is not a linear program, write a sentence or two explaining why. Note: to make your answers easier to mark, please order your vector of vari- ables by subscript. If 2 variables have the same subscript (because you have split a variable x; into x and x) list x first followed by x. For example: x¹ = (x1, T2, x3, x,x, x5) is ordered as described. (a) (b) (c) minimize 5x1 + 6x3 subject to 2.9x1 + 6x2 + 8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x₁18x2 ≤ 14, X1, X2, X3 20 maximize subject to 5x₁(1 − 3x₂ + x3) - X₂ x₁ + 3x2 + x3 ≥ 4, -X₁ + X₂ X3 ≤ 3, -2x1 + x₂ ≤ 7, X1, X2, X3 20 maximize 2x1 + x2x3 subject to 4x₁ + x₂ + 3x3 ≤ 1, -2x₂ + x3 ≤ 1, 4x2 + 2x3 = -7, ₁ unrestricted, X₂ ≤ 0, X3 20
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