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Unit 2: Linear Programming Problems




          Step 3: Graph the data                                                                Notes






















          Step 4: Find the co-ordinates of the corner points

                     Corner Points                x1                    x2
                         A                        70                    0
                         B                        20                    25
                         C                        10                   33.33
                         D                        0                     50

                     At ‘B’ 100x  + 200x  = 7,000                                 …..(1)
                              1     2
                            50x  + 60x  = 2,500                                   …..(2)
                               1    2
          Divide eq. (1) by 2, we get,

                           50x  + 100x  = 3,500
                              1     2
                            50x  + 60x  = 2,500
                               2    2
                                  40x  = 1,000
                                    2
          Therefore                x  = 25
                                    2
          Put                      x  = 25 in eq. (2), 50x  + 60(25) = 2,500
                                    2               1
                           50x  + 1,500 = 2,500
                              1
                                 50x  = 1,000
                                    1
          Therefore                x  = 20
                                    1
          At                      ‘C’ = 100x  + 60x  = 3,000                      …..(1)
                                           1    2
                            50x  + 60x  = 2,500                                   …..(2)
                               1    2
                                 50x  = 500
                                    1
          Therefore                x  = 10
                                    1
          Put                      x  = 10 in eq. (2)
                                    1
                          50(10) + 60x  = 2,500
                                    2
                                 60x  = 2,000
                                    2
          Therefore                x  = 33.33
                                    2



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