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File: Programming Pdf 175567 | Finite Math Ch4 3 Workbook
22 section 4 3 the simplex method and the standard maximization problem question 1 what is a standard maximization problem question 2 what are slack variables question 3 how do ...

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                                                                                                   22 
               
              Section 4.3 The Simplex Method and the Standard Maximization Problem 
              Question 1 – What is a standard maximization problem? 
              Question 2 – What are slack variables? 
              Question 3 - How do you find a basic feasible solution? 
              Question 4 - How do you get the optimal solution to a standard maximization problem with the 
                          Simplex Method? 
              Question 5 - How do you find the optimal solution for an application? 
               
              Question 1 – What is a standard maximization problem? 
              Key Terms 
              Standard maximization problem 
              Summary 
              A standard maximization problem is a type of linear programming problem in which the 
              objective function is to be maximized and has the form 
                                               z=ax +ax ++ax
                                                   11 22          nn
                                                                      
                    a,,a                       xx,,
              where  1     n  are real numbers and  1  n  are decision variables. The decision variables 
              must represent non-negative values. The other constraints for the standard maximization problem 
              have the form 
                                              bx+bx++bx≤c
                                               11 22          nn  
                    bb,,                             c ≥ 0
              where  1     n  and c are real numbers and  . 
              The variables may have different names, but in standard maximization problems four elements 
              must be present: 
                 1.  The objective function is maximized. 
                 2.  The objective function must be linear. 
                 3.  The constraints are linear where the variables are less than or equal to a nonnegative 
                     constant. 
                 4.  The decision variables must be nonnegative. 
               
                                                 23 
        
                                                   
        
       Notes 
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
                                                                                                24 
              
             Guided Example                                Practice 
              Is the linear programming problem 
               
                                                 Maximize z =5xx6 +
                                                               12
                                                 subject to
                                                          2xx+≤4
                                                            12  
                                                          xx+≤24
                                                           12
                                                          xx≥0,   ≥0
                                                           12
               
              a standard maximization problem? 
               
              Solution To see whether this linear programing problem is a standard linear programming problem, 
              check the requirements above. 
                                                                              The objective function has the 
                      The objective function                 = +
                                                                xx
                                               Maximize z 5        6
                      is maximized                              12 form                          
                                               subject to
                                                            +≤                 All constraints have the form 
                                                          xx
                                                         24
                                                           12  
                                                           +≤                             where c is 
                                                         xx
                                                             24
                                                          12                   nonnegative. 
                                                           ≥≥
                                                         xx
                                                             0,    0
                                                          12 Decision variables are 
                                                                             nonnegative 
               
              Since all the requirements are met, this is a standard minimization problem. 
               
              
              
              
              
              
              
              
              
              
              
                                                                                           25 
              
              1.  Is the linear programming problem 
               
                                               Maximize z =3xx4 +
                                                            12
                                               subject to
                                                       xx+≤40  
                                                        12
                                                       xx+≤2   60
                                                        12
                                                       xx≥0,   ≥0
                                                        12
                                                         
              a standard maximization problem? 
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
              
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...Section the simplex method and standard maximization problem question what is a are slack variables how do you find basic feasible solution get optimal to with for an application key terms summary type of linear programming in which objective function be maximized has form z ax nn xx where n real numbers decision must represent non negative values other constraints have bx c bb may different names but problems four elements present less than or equal nonnegative constant notes guided example practice maximize subject see whether this programing check requirements above all since met minimization...

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