For the primal and the associated dual problems shown below, use the complementary slackness theorem tofind the optimal value of y2 given that the optimal solution of the primal problem is x1=0, x2-4/3, x3=1-Maximize 4x1subject to6x2-5x32x1+ 3x3 ≥ 33x2+ 2x3 ≥ 6X1,X3 ≥ 0.Minimize 3y₁ + 6y₂Subject toY₁ ≥-2Y₂ ≥-23y₁ + 2y₂2-53₁ ≤0Y/₂ ≤0Answer: 0x2,

Given: x1 = 0 , x2 = 4/3 , x3 = 1 Maximize , -4x1-6x2-5x3 Subject to 2x1 +3x3 ≥3 3x2+2x3≥6x1,x2,x3…

Answered: For the primal and the associated dual…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Q1. Given the following multi-objective problem (A): max 2X, + 0.5X2 + Xҙ (Z1) (Z2) (Z3) min 4X1 – 3X2 + X3 min X2 – 2X3 s.t. (1) 4X1 + X3 < 10 5X1 + X2 < 20 X; are non-negative Formulate this problem using Global Criterion (GC) method and Compromise Programming (GP) method.
For the feasible set in the figure to the right, determine x and y so that the objective function 8x +3y is maximized. (0,20) x= x-J.y-O = feasible (0,0) set (20,0) Q
QUIZ 5.docx Operation Research QUIZ 5 Q.NO.1.Find the dual of following question .Also find its optimal Solution. Z = 2x1 + 3x2 + X3 b) s/t max X1 + 2x2 + X3 <20 2 4 X2 +4x; = 10 X + X2 with x1, X2, X3 0.
Consider the following LP model and it is graphical solution to answer questions from a) to g). Maximize z= 4x,+5x2 Subject to: X:5 .(1) 2x:+X;512 ..(2) X,+2x;s12 ..(3) X1, X220.. .(4) 12 11 10 D A *9 10 11 12 n a) What is the optimal solution x1, X2 and z? b) Determine the optimality range of the objective function coefficient c1. c) Determine the feasibility range of the right-hand side for constraint 1, 2 and 3. d) How many basic feasible solutions in this problem? e) Is there any binding constraint(s)? f) Dose any constraint has a slack? which one and by how much? g) Dose any constraint has a surplus? which one and by how much?
A function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.
Find the Optimal solution for the below Linear Program by Simplex method: Maximize Z = 200x + 80y +60z Subject to x + y + z <= 100 10x + 2y + 5z <= 600 2x + 2y + 3z <= 300 x, y, z >= 0
Ex. 3 Consider the following problem: Maximize 2x1 subject to + x2 x1 + 2x2 2x1 + 3x2 - X3 +6x3 + 4x3 - - 4x4 x4 + x4 + x3 x4 x1 x1, X2, x3, x4 VI VI VI ɅI ≤ 6 0. Find a basic feasible solution with the basic variables as x1, x2, and x4. Is this solution optimal? If not, then starting with this solution find an optimal solution.
Solve the linear programming problem by the simplex method. Maximize P = 16x + 13y subject to x + y ≤ 12 3x + y ≤ 30 10x + 7y ≤ 70 x ≥ 0, y ≥ 0 The maximum is P = at (x, y) = .
Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decision variables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2 decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values and ranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Round your answers to 2…
Consider the problem ari + br2 subject to a?+ = 2 maximize where a and b are real numbers. Show that if [1, 1]" is an optimizer to the problem, then a = b.
• Consider the following LP: maximize 2x1 + 5x2 s.t. -x1 + 2x2 < 5 2x1 + 3x2 < 12 X1 + x2 2 -1 X1, X2 2 0 1. Write the dual problem. 2. Solve the optimal solution for the primal problem. 3. Find the optimal dual solutions by complementary slackness.
Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Subject to: Z= 1X₁ + 1X₂ 2x, +1X, 572 1X₁ + 2X₂ ≤72 X₁Xx₂ 20 (C₁) (C₂) Use computer software to solve the LP model The optimum solution is: X₁ = (round your response to two decimal places) (round your response to two decimal places) Optimal solution value Z = b) If a technical breakthrough change, the optimal solution (round your response to two decimal places) occurred that raised the profit per unit of X, to $3, due to this (Use sensitivity table to answer this question.) e) If the impact of technical breakthrough was incorrectly determined and instead of X, profit coefficient increasing to $3 it only increases to $1.10. As a result of this correction, the optimal solution found originally (Use sensitivity table to answer this question) 120- 110 100 10 80 rokids 20 50 304 20 16 0 soprofe Line 20 30 40 50 60 70 80 90 100 110 120 X1 860 G

SEE MORE QUESTIONS

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,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS