1. Minimi [Ans. X1 max 2. Maximize Z = x+ x subject to x, + x, S 4, 2x, + x, S 6, x, + 3x, S 6, and [Ans. Zmax = 10; x, = 3, x, = 1] dr2+ 9r?< 36, 2x, + 3x, 2 6, and x, 20, 0Sx, S1. %3D X 2 0. %3D
1. Minimi [Ans. X1 max 2. Maximize Z = x+ x subject to x, + x, S 4, 2x, + x, S 6, x, + 3x, S 6, and [Ans. Zmax = 10; x, = 3, x, = 1] dr2+ 9r?< 36, 2x, + 3x, 2 6, and x, 20, 0Sx, S1. %3D X 2 0. %3D
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
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Solve question 2 only plz solve every step how u draw the garph..
![8. How
examples of
(a) Multiple optimal solutions
(b) Infeasible solutions
(c) Infinite solutions.
is unbounded solution? How is it different from multiple solutions and infeasib
solutions?
ay are unrestricted variables treated in graphical solutions? Where do you get the
feasible regions if unrestricted variables exist in NLPPS?
I3 Give step-by-step procedure of the graphical method of solving optimization
problems.
14. List the merits and demerits of graphical methods for using optimization techniques.
15. Explain the different types of constraint surfaces that occur in graphical solutions.
Formulation and Computational Exercises
1. Minimize Z = 2x, +x, subject to x + xs 16, x, + x, 2 4, and x,, x, 2 0.
[Ans. x, = 4, x, = 0; Zax = 8]
x + x subject to x, + x, < 4, 2x, + x, S 6, x, + 3x, s 6, and
2. Maximize Z =
%3D
X, X2 2 0.
3. Maximize Z = /3x, + 1.5x, subject to 4x?+9x;< 36, 2x, + 3x, 2 6, and x, 2 0, 0 <x, S 1.
[Ans. Zmax = 10; x = 3, x, = 1]
%3D
[Ans. x, = 3/3/2, x, = 1; Zmax = 9/2 +3/2 = 6]
4. Maximize Z = x} + 2x; subject to x + 4x, 2 0, 7x, - 4x, 2 20, and x,, x2 2 0.
5. Maximize Z = x, + 2x, subject to -2x, + x < 0, 2x, + x 2 0, and 0 < x, S 3,
X, unrestricted.
6. Maximize Z = 3x, + 3x, subject to 9x² + 4x3 < 36, 2x, < 3, both x,, X2 unrestricted.
[Ans. x, = 4, x, = 2; Zma = 16 + 8 = 24]
max
[Ans. x, = 4.5, x, = 3; Zmax
10.5]
7. Maximize Z = 2x, + 3x, subject to -x? + x3- 6x, + 5 < 0, 2V3x, + 3x, s 18, and
%3D
[Ans. x, = 1.17, x2 = 2.5: Zmax
= 11 (approx.)]
[Ans. Multiple solution
V3, x, = 4; or x, = (5/3 )/7, x, = 32/7; Zmax
%3D
6V31](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3932aa1c-1b5f-4d84-a3d3-4f7705949611%2Fda7cfcc8-d4b9-4130-90a4-34e7954e5f38%2Ftom8crc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. How
examples of
(a) Multiple optimal solutions
(b) Infeasible solutions
(c) Infinite solutions.
is unbounded solution? How is it different from multiple solutions and infeasib
solutions?
ay are unrestricted variables treated in graphical solutions? Where do you get the
feasible regions if unrestricted variables exist in NLPPS?
I3 Give step-by-step procedure of the graphical method of solving optimization
problems.
14. List the merits and demerits of graphical methods for using optimization techniques.
15. Explain the different types of constraint surfaces that occur in graphical solutions.
Formulation and Computational Exercises
1. Minimize Z = 2x, +x, subject to x + xs 16, x, + x, 2 4, and x,, x, 2 0.
[Ans. x, = 4, x, = 0; Zax = 8]
x + x subject to x, + x, < 4, 2x, + x, S 6, x, + 3x, s 6, and
2. Maximize Z =
%3D
X, X2 2 0.
3. Maximize Z = /3x, + 1.5x, subject to 4x?+9x;< 36, 2x, + 3x, 2 6, and x, 2 0, 0 <x, S 1.
[Ans. Zmax = 10; x = 3, x, = 1]
%3D
[Ans. x, = 3/3/2, x, = 1; Zmax = 9/2 +3/2 = 6]
4. Maximize Z = x} + 2x; subject to x + 4x, 2 0, 7x, - 4x, 2 20, and x,, x2 2 0.
5. Maximize Z = x, + 2x, subject to -2x, + x < 0, 2x, + x 2 0, and 0 < x, S 3,
X, unrestricted.
6. Maximize Z = 3x, + 3x, subject to 9x² + 4x3 < 36, 2x, < 3, both x,, X2 unrestricted.
[Ans. x, = 4, x, = 2; Zma = 16 + 8 = 24]
max
[Ans. x, = 4.5, x, = 3; Zmax
10.5]
7. Maximize Z = 2x, + 3x, subject to -x? + x3- 6x, + 5 < 0, 2V3x, + 3x, s 18, and
%3D
[Ans. x, = 1.17, x2 = 2.5: Zmax
= 11 (approx.)]
[Ans. Multiple solution
V3, x, = 4; or x, = (5/3 )/7, x, = 32/7; Zmax
%3D
6V31
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