Text: D. A. Piee, Optimization Theory with Applications. Dover, 1986Problem XXXXXXXXXXfor this...

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Text: D. A. Piee, Optimization Theory with Applications. Dover, 1986Problem XXXXXXXXXXfor this problem you can use simplex method – it was used frequently during courseProblem-2Problem-3

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Text: D. A. Pierre, Optimization Theory with Applications. Dover, 1986 
Problem-1         for this problem you can use simplex method – it was used frequently during 
course
Problem-2
Problem-3
1. Given , 
Max P = 3x1-x2-4x3 
subjected to  
{
          
          
                 
 
the given constraints can also be written as, 
{
 
 
 
 
          
       
        
      

With max P-3x1+x2+4x3 
Introducing the slack variables to remove the inequality, we have 
max P-3x1+x2+4x3 
subjected to  
{
 
 
 
 
             
          
           
         

Creating the first simplex tableau 
p x1 x2 x3 s1 s2 s3 s4 s5 b 
1 -3 1 4 0 0 0 0 0 0 
0 1 1 -1 1 0 0 0 0 4 
0 1 -1 0 0 1 0 0 0 2 
0 -1 1 0 0 0 1 0 0 2 
0 0 0 -1 0 0 0 1 0 -1 
0 0 0 1 0 0 0 0 1 -1
The element in blue is the pivot element. For corresponding row operations,

Text: D. A. Pierre, Optimization Theory with Applications. Dover, 1986 Problem XXXXXXXXXXfor this problem you can use simplex method – it was used frequently during course Problem-2 Problem-3

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