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Solve the problem using simplex algorithm Max Z= 6X+6Y S.T X+3Y≤2 2X+2Y≤5 X,Y≥0

Solve the problem using simplex algorithm Max Z= 6X+6Y S.T X+3Y≤2 2X+2Y≤5 X,Y≥0

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 problem using simplex algorithm
Max Z= 6X+6Y
S.T
X+3Y≤2
2X+2Y≤5
X,Y≥0

Expert Solution
Step 1

The given linear programming problem is

                                 Maximize Z=6x+6y

                                 Subject to x+3y⩽2

                                                 2x+2y⩽5

                                                  x,y⩾0

Introducing two slack variables s1 and s2 into the 1st and 2nd constraints respectivly,then the problem can be re-write as

                            Maximize Z=6x+6y+0s1+0s2

                             Subject to   x+3y+s1=2

                                               2x+2y+s2=5

                                                x,y,s1,s2⩾0

Let us choose s1 and s2 as a basic variable ,then the non-basic variable x=0 , y=0 and s1=2 , s2=5

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