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 at first followed by . For example: x¹ = (x₁, ₂, x3, x, a, 5) is ordered as described. (a) 5x1 + 6x3 2.91 +6x2 +8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x118x₂ ≤ 14, 1, T2, T3 20 (b) (c) minimize subject to maximize subject to 5x1(1-3x2 + x3) - I2 x1 + 3x2 + x3 24, -₁ + ₂x3 ≤ 3, -2x1 + x₂ ≤7, T1, T2, T3 20 maximize 2x₁ + ₂-3 subject to 4x₁ + x₂ + 3x3 ≤ 1, -2x2 + x3 ≤ 1, 4x2 + 2x3 = = -7, ₁ unrestricted, ₂ ≤ 0, T3 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 at first followed by . For example: x¹ = (x₁, ₂, x3, x, a, 5) is ordered as described. (a) 5x1 + 6x3 2.91 +6x2 +8x3 ≥ 6.2, (x₁ - x3)² ≥ 16, 1.5x118x₂ ≤ 14, 1, T2, T3 20 (b) (c) minimize subject to maximize subject to 5x1(1-3x2 + x3) - I2 x1 + 3x2 + x3 24, -₁ + ₂x3 ≤ 3, -2x1 + x₂ ≤7, T1, T2, T3 20 maximize 2x₁ + ₂-3 subject to 4x₁ + x₂ + 3x3 ≤ 1, -2x2 + x3 ≤ 1, 4x2 + 2x3 = = -7, ₁ unrestricted, ₂ ≤ 0, T3 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: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 a first followed by . For example:
x¹ = (x₁, T₂, x3, x,x, xs) is ordered as described.
(a)
(b)
(c)
minimize
subject to
maximize
subject to
maximize
subject to
5x1 + 6x3
2.9x1 + 6x2 +8x3 ≥ 6.2,
(T₁ - 3)² ≥ 16,
1.5x₁18x2 ≤ 14,
I1, I2, I3 20
5x1(1-3x2 + x3) - I2
x1 + 3x2 + x3 ≥ 4,
-X₁ + X₂ X3 ≤ 3,
-2x1 + x₂ ≤7,
I1, I2, I3 20
2x₁ + x₂ −X3
4x₁ + x₂ + 3x3 ≤ 1,
-2x₂ + x3 ≤ 1,
4x2 + 2x3 = -7,
₁ unrestricted,
X₂ ≤ 0,
T3 20
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 34 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
