Solve a linear problem using bounded variables method
  
 
     
     
             
                 
 
 
         
         0 
         
 
         
             
         
 
 
 
 
             
 
             
 
     $begingroup$ 
     
 
 Consider the following   $$min 3x_1+4x_2\ s.t. 4x_1+3x_2ge12 \ 3x_1+4x_2le12\ x_1,x_2ge0$$   Substitute the first restriction by $x_1le3$  and solve the LP by bounded variable method.   Attempt   We first standarize and then set in a table   begin{array}{r|rrrrr|r}             & x_1 & x_2 & x_3 & x_4 &    \ hline         z &   -3 &   -4 &   0 &   0 &   & 0 \ hline         x_3 &   -4 &  -3 &   1 &   0 &   & -12 \         x_4 &   3 &   4 &   0 &   1 &  & 12             end{array}   From here we see that $theta_1=min{12/4}=3$   $theta_2=min{frac{-12-?}{-3}}=?$   and $u_2=?$   The bounded variable method requires an upper bound of  $x_3$  but does not have.   How will I find $theta_2$ ? $u_2?$   Could someone help...