Essay About Jefferson City And Optimal Solution

Management Chapter 6 Problem 2
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CHAPTER 6 PROBLEM 2Let us define our variables:X11 = Quantity shipped from  Jefferson City to Des MoinesX12 = Quantity shipped from  Jefferson City to Kansas CityX13 = Quantity shipped from  Jefferson City to St. LouisX21= Quantity shipped from  Omaha to Des MoinesX22= Quantity shipped from  Omaha to Kansas CityX23= Quantity shipped from  Omaha to St. LouisObjective function:Min 14X11 + 9X12+ 7X13+8X21+10X22+5X23Subject to:X11       +   X12          +       X13                                                              <=    30                                                             X21   +  X22    +       X23            <=     20X11                                                 +   X21                                               =       25                   X12                                             + X22                                  =       15                                           X13                                    +      X23              =       10X11, X12, X13, X21, X22. X23 >= 0  (greater or equal to 0)Optimal solution using solver in excel:5 units  have to be shipped from Jefferson city to Des Moines for a cost of $7015 units have to be shipped from Jefferson City to Kansas for a cost of $13510 units have to be shipped from Jefferson City  to St Louis for a cost of $1020 units have to be shipped from Omaha to  Des Moines for a costo f $1600 units Will be shipped from Omaha to Kansas City0 units will be shipped from Omaha to St LouisFollowing this combination, our optimal solution will lead us to a minimum total cost of $435CHAPTER 6 PROBLEM 3A.[pic 1]500        10        400[pic 2][pic 3][pic 4][pic 5][pic 6][pic 7][pic 8]        20[pic 9][pic 10]        200400                 12               15[pic 11]        15        18        300B. Let us define our variables:X11 = Quantity shipped from  Southern Gas to  HamiltonX12 = Quantity shipped from  Southern gas to ButlerX13 = Quantity shipped from  Southern gas to ClermontX21= Quantity shipped from  Northwest gas to HamiltonX22= Quantity shipped from  Northwest gas to ButlerX23= Quantity shipped from  Northwest gas to ClermontObjective function:Min 10X11 + 20X12+ 15X12+12X21+15X22+18X23Subject to:X11       +   X12          +       X13                                                              <=    500                                                             X21   +  X22    +       X23            <=     400X11                                                 +   X21                                               =       400