b) Consider the following mixed constrained LP problem.Minimize z = 4x, +x2%3DSubject to3x1 + x2 = 34x1 + 3x2 2 6X1 + 2x2 <4X1, X2 2 0For the following questions, use the Big-M method:a) Give the initial tableau to the above LP.b) Perform one iteration and give the improved basic feasible solution.

Answered: Image /qna-images/answer/8a2395ea-84df-4d10-9ee3-2e9909361043.jpg

Answered: b) Consider the following mixed…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
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 following problem. Maximize Z = -X1 - X2, subject to x₁ + x₂ ≤ 8 x₂ ≥ 3 -x₁ + x₂ ≤2 and x₁ ≥ 0, X₂ ≥ 0. (a) Solve this problem graphically. (b) Use the dual simplex method manually to solve this problem. (c) Trace graphically the path taken by the dual simplex method.
Consider the following LP model: max 10x1 + 12x2 + s.t. x1 2x1 2x1 + + + X2 + 2x2 + 2x3 + 2x3 2x2 + X3 X 12x3 ≤20 0 Use the simplex method and find the optimal solution for this problem. (You need to determine the objective value, the basic and non-basic variables and their values.)
1.1) Use revised simplex method to solve the following lineur programing problem. Maximize Z = x₁ + x₂ + x3 Subject to X₁-24-2x6=5 x2 + 2x14-3x5 + x6 =3 x3 t2x45xs +bxb=5 aj zo.
2. Solve the optimal solution (if there are any) for the following LP problem using Two-phase method. Minimize Z= 2x₁ - 4x₂ + 3x3 subject to 5x₁-6x₂+2x325 -x₁ + 3x₂ + 5x328 2x₁ + 5x₂ - 4x3 ≤9 x₁ ≥ 0, x₂ ≥ 0, x3 ≥0
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
6. Consider a constrained optimisation problem with the objective function f(x) = 3x + 2y and the constraint 2x+y=10. Find the maximum value of f(x) within the feasible region.
Solve the following LP problem by hand using the Simplex Method. Problem: Maximize: x + 5y subject to: 7y – 12x 0, y > 0
Solve the following LP problems: 1. Maximize z = 1x₁ + 2x₂ + 3x3 Subject to: 1x₁-2x₂ + 3x3 ≤ 10 x₁ + 2x₂ ≤ 5 x₁ ≤ 1 X₁, X₂, X3 ≥ 0 Requirements: Using the LP simplex method, identify three alternative optimal basic solutions of this problem.
a) Consider the following LP problem. Maximize z = 2x1 + x2 subject to 4x, + 3x2 s 12 4x1 + x2 < 8 4x1 + 2x2 5 8 X1, X2 2 0 Use the simplex approach to determine its optimal solution and state the special case(s) involved, if any.

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