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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, X2, X3, X, x, x5) is ordered as described. (a) minimize subject to 5x1 +6x3 2.9x1 + 6x2 + 8x3 ≥ 6.2,

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, X2, X3, X, x, x5) is ordered as described. (a) minimize subject to 5x1 +6x3 2.9x1 + 6x2 + 8x3 ≥ 6.2,

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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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, X2, X3, X1, X , I 4,x4, x5) is ordered as described. (a) minimize subject (b) (c) maximize subject to maximize subject to 5x1 + 6x3 2.9x1 + 6x2 +8x3 ≥ 6.2, (x1 - x3)² ≥ 16, 1.5x118x2 ≤ 14, X1, X2, X3 > 0 5x₁(1 − 3x2 + x3) x₁ + 3x2 + x3 ≥ 4, -X1 + X₂ X3 ≤ 3, -2x1 + x₂ ≤ 7, X1, X2, X3 ≥ 0 2x1 + x2 X3 4x1 + x2 + 3x3 ≤ 1, -2x2 + x3 ≤ x1, 4x2 + 2x3 = -7, X2 x₁ unrestricted, X₂ ≤ 0, X3 ≥ 0
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, X2, X3, X1, X , I 4,x4, x5) is ordered as described. (a) minimize subject (b) (c) maximize subject to maximize subject to 5x1 + 6x3 2.9x1 + 6x2 +8x3 ≥ 6.2, (x1 - x3)² ≥ 16, 1.5x118x2 ≤ 14, X1, X2, X3 > 0 5x₁(1 − 3x2 + x3) x₁ + 3x2 + x3 ≥ 4, -X1 + X₂ X3 ≤ 3, -2x1 + x₂ ≤ 7, X1, X2, X3 ≥ 0 2x1 + x2 X3 4x1 + x2 + 3x3 ≤ 1, -2x2 + x3 ≤ x1, 4x2 + 2x3 = -7, X2 x₁ unrestricted, X₂ ≤ 0, X3 ≥ 0
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