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 xt first followed by x. For example: x = (x1, 2, x3, x, x,x5) is ordered as described. (a) 5x1 + 6x3 2.9x1 + 6x2 +8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x118x2 14, X1, X2, X30 (b) O minimize subject to maximize subject to maximize subject to 5x1(1-3x2 + x3) = x2 x1 + 3x2 + x3 ≥ 4, -x1 + x₂-x3 ≤ 3, -2x1 + x₂ ≤ 7, X1, X2, X30 2x1x2x3 4x1 + x2 + 3x3 ≤ 1, -2x2 + x3 ≤ x1, 4x2 + 2x3 = -7, ₁ unrestricted, X₂ ≤ 0, X3 20
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 xt first followed by x. For example: x = (x1, 2, x3, x, x,x5) is ordered as described. (a) 5x1 + 6x3 2.9x1 + 6x2 +8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x118x2 14, X1, X2, X30 (b) O minimize subject to maximize subject to maximize subject to 5x1(1-3x2 + x3) = x2 x1 + 3x2 + x3 ≥ 4, -x1 + x₂-x3 ≤ 3, -2x1 + x₂ ≤ 7, X1, X2, X30 2x1x2x3 4x1 + x2 + 3x3 ≤ 1, -2x2 + x3 ≤ x1, 4x2 + 2x3 = -7, ₁ unrestricted, X₂ ≤ 0, X3 20
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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 xt first followed by x. For example:
x¹ = (x1, 2, x3, x, x,x5) is ordered as described.
(a)
5x1 + 6x3
subject to 2.9x1 + 6x2 +8x3 ≥ 6.2,
(x₁ - x3)² ≥ 16,
1.5x118x2 ≤ 14,
X1, X2, X30
(b)
O
minimize
maximize
subject to
5x1(13x2 + x3) - X2
x₁ + 3x2 + x3 ≥ 4,
-X1 + x₂-x3 ≤ 3,
-2x1 + x₂ ≤ 7,
X1, X2, X30
maximize 2x1 + x2x3
subject to
4x1 + x2 + 3x3 ≤ 1,
-2x₂ + x3 ≤ x1,
4x2 + 2x3 = -7,
₁ unrestricted,
X₂ ≤ 0,
X3 20
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