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Solve the following optimization problem using algebraic methods. Maximise f(x1,x2)=3x1+2x2 subjectto: x1 + x2 ≤ 5, −x1 + 2x2 ≤ 4, x1,x2 ≥0.   Write down the initial augmented matrix and the subsequent ma- trices from which you obtain the basic solutions.

Solve the following optimization problem using algebraic methods. Maximise f(x1,x2)=3x1+2x2 subjectto: x1 + x2 ≤ 5, −x1 + 2x2 ≤ 4, x1,x2 ≥0.   Write down the initial augmented matrix and the subsequent ma- trices from which you obtain the basic solutions.

Advanced Engineering Mathematics
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 optimization problem using algebraic methods. Maximise f(x1,x2)=3x1+2x2 subjectto:

x1 + x2 ≤ 5,

−x1 + 2x2 ≤ 4,

x1,x2 ≥0.

 

  • Write down the initial augmented matrix and the subsequent ma- trices from which you obtain the basic solutions.

 

Expert Solution
Step 1

We have to add the slack and surplus variables to convert the given linear

programming problem into the standard form.

After adding the slack variables (as the constraints are of ≤ type), we get,

Maximize fx1, x2=3x1+2x2 subject to

x1+x2+x3=5-x1+2x2+x4=4x1, x2, x3, x4≥0

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