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 = (1, 2, x3, x, x₁, x5) is ordered as described. (a) (b) (c) minimize subject to maximize 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 2 X₁ + 3x2 + x3 ≥ 4, -X₁ + X₂ X3 ≤ 3, -2x1 + x₂ ≤7, X1, X2, X3 20 2x₁ + x₂ - X3 4x₁ + x2 + 3x3 ≤ 1, -2x₂ + x3 ≤ x1, 4x2 + 2x3 = -7, ₁ unrestricted, X₂ ≤ 0, X3 ≥ 0
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 = (1, 2, x3, x, x₁, x5) is ordered as described. (a) (b) (c) minimize subject to maximize 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 2 X₁ + 3x2 + x3 ≥ 4, -X₁ + X₂ X3 ≤ 3, -2x1 + x₂ ≤7, X1, X2, X3 20 2x₁ + x₂ - X3 4x₁ + x2 + 3x3 ≤ 1, -2x₂ + x3 ≤ x1, 4x2 + 2x3 = -7, ₁ unrestricted, X₂ ≤ 0, X3 ≥ 0
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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Transcribed Image Text: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, x4, 25) 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, X30
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 ≥ 0
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