Solve the following LP problems:1. Maximize z = 1x₁ + 2x₂ + 3x3Subject to: 1x₁-2x₂ + 3x3 ≤ 10x₁ + 2x₂ ≤ 5x₁ ≤ 1X₁, X₂, X3 ≥ 0Requirements: Using the LP simplex method,identify three alternative optimal basicsolutions of this problem.

In the given question a linear programming problem is given. We have to solve by simplex method.…

Answered: Solve the following LP problems: 1.…

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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Solve the following nonstandard maximum problem: Maximize P = 3x1 + x2 subject to the constraints: x₁ + x₂ ≤ 8 5x1 + 3x2 2 36 7x1 + 4x2 2 14 X₁ ≥ 0, X₂ 20 The maximum of the objective function is reached at the point: a. X₁ = 2, X₂ = 2 b. X111, X2 = 2 C. X1 = 6, X₂ = 2 d. x₁ = 2, X₂ = 6 O C C с
b) Consider the following Linear Programming (LP) problem: Maximize z = 3x₁ + 2x2 Subject to 2x₁ + x₂ ≤2 3x₂ + 4x₂ 2 12 X₁, X₂ 20 Using the Two-Phase method, determine the optimal solution (specify the special case(s) involved, if any).
Need only a handwritten solution only (not a typed one).
2. Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. b) Maximize z = 3x₁ + 2x2 Subject to: 4x11x28 4x1 + 3x2 ≤ 12 4x1 + 1x2 ≤8 X1, X2 ≥ 0
Solve the following LPP problems using Simplex Method: 4. Max Z = X1 - 3 X2 + 2x3 Subject to 3x1 - X2+ 2x3 =0
Use the simplex method and the Duality Principle to solve the following minimum problem: (see image below) and using your final tableau answer the questions below by entering the correct answer in each blank box.
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.
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. (see image) Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is:
2. Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2X1 X2 ≤2 3x14x2 ≤ 8 X1, X2 ≥ 0
Solve the following LP problem by hand using the Simplex Method. Problem: Maximize: x + 5y subject to: 7y – 12x 0, y > 0

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Solve the following LP problems: 1. Maximize z = 1x₁ + 2x₂ + 3x3 Subject to: 1x₁ - 2x₂ + 3x3 ≤ 10 x₁ + 2x₂ ≤ 5 x₁ ≤ 1 X₁, X₂, X₂ ≥ 0 Requirements: Using the LP simplex method, identify three alternative optimal basic solutions of this problem.