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4. Using the Simplex Method, solve: Maximize 5x1+x2 3x12x2 ≤ 6 subject to -401 + 2x2 ≤4 x1, x2 ≥ 0 (ID vita

4. Using the Simplex Method, solve: Maximize 5x1+x2 3x12x2 ≤ 6 subject to -401 + 2x2 ≤4 x1, x2 ≥ 0 (ID vita

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 13RE
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Please follow how the example was given in the other photo to solve this LPP using simplex method. This was is easier and short for me to understand
Put in Standform Basic feascal Solution To phase Method Ex 2: Solve the LP problem weing the simplex Method: Max 84: J 5x + 6x₂ S3x₁ + 4x₂ = 18 2x₁ + x₂ < 7 X₁, X270 Soln: 1st transform the LP problem into standard form bv X3 X4 Construct the initial Initial min 5x - 6x₂ & √3x₁ + 4x₂ + x3 = 18 2x₁ + x₂ + x4 = 7 -х, ха, хз, х4 70 X₁ is NOI -S X₂ 4 Current basis XB = b.f.s 1 -6 X3 1 O Ⓒ } 000円 tableau X4 20-0 O Using the Simplex Metud b 18 7 O [93 94] = [0] (₂=-6 min ~ { b², 9:₂>0} = min [18, +} = 2 The two-phase Simplex Method There are two times when an 4 probleem has no starting bifis and thus, the simplex method canot be readily initiated. Thus, there is a need to a systemic method to find LP problem. The Two- Method an require Starting bifs to such -phase Such method Example: be the simplex method to solve min 2x₁ + 3x₂ Slo: 1st Sit a 4x + 2x₂ > 12 X₁ + 4x₂ > 6 X₁, X₂ 70 transform min sit 9 which occurs in row I is the 2x + 3x₂ 4рх, +2х2 - Хз - 12 X₁ + 4x₂ - X = 6 X₁, X2, X3, X470 problem in standard form : There is basis matrix since on the f.T- no for tp problem would imply there is a bifus. But Such a Solution would have been (00X3 X4) ! But X3 = -12 and Xq = -6 which is feasible. none of
Transcribed Image Text:Put in Standform Basic feascal Solution To phase Method Ex 2: Solve the LP problem weing the simplex Method: Max 84: J 5x + 6x₂ S3x₁ + 4x₂ = 18 2x₁ + x₂ < 7 X₁, X270 Soln: 1st transform the LP problem into standard form bv X3 X4 Construct the initial Initial min 5x - 6x₂ & √3x₁ + 4x₂ + x3 = 18 2x₁ + x₂ + x4 = 7 -х, ха, хз, х4 70 X₁ is NOI -S X₂ 4 Current basis XB = b.f.s 1 -6 X3 1 O Ⓒ } 000円 tableau X4 20-0 O Using the Simplex Metud b 18 7 O [93 94] = [0] (₂=-6 min ~ { b², 9:₂>0} = min [18, +} = 2 The two-phase Simplex Method There are two times when an 4 probleem has no starting bifis and thus, the simplex method canot be readily initiated. Thus, there is a need to a systemic method to find LP problem. The Two- Method an require Starting bifs to such -phase Such method Example: be the simplex method to solve min 2x₁ + 3x₂ Slo: 1st Sit a 4x + 2x₂ > 12 X₁ + 4x₂ > 6 X₁, X₂ 70 transform min sit 9 which occurs in row I is the 2x + 3x₂ 4рх, +2х2 - Хз - 12 X₁ + 4x₂ - X = 6 X₁, X2, X3, X470 problem in standard form : There is basis matrix since on the f.T- no for tp problem would imply there is a bifus. But Such a Solution would have been (00X3 X4) ! But X3 = -12 and Xq = -6 which is feasible. none of
Using the Simplex Method, solve: Maximize 5x1 + x2 3x12x26 subject to-4x1+2x2 ≤ 4 x1, x2 > 0 (10210 gast. V
Transcribed Image Text:Using the Simplex Method, solve: Maximize 5x1 + x2 3x12x26 subject to-4x1+2x2 ≤ 4 x1, x2 > 0 (10210 gast. V
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