Management Chapter 6 Problem 2

CHAPTER 6 PROBLEM 2

1. Let us define our variables:

X11 = Quantity shipped from  Jefferson City to Des Moines

X12 = Quantity shipped from  Jefferson City to Kansas City

X13 = Quantity shipped from  Jefferson City to St. Louis

X21= Quantity shipped from  Omaha to Des Moines

X22= Quantity shipped from  Omaha to Kansas City

X23= Quantity shipped from  Omaha to St. Louis

Objective function:

Min 14X11 + 9X12+ 7X13+8X21+10X22+5X23

Subject to:

X11       +   X12          +       X13                                                              <=    30

                                                             X21   +  X22    +       X23            <=     20

X11                                                 +   X21                                               =       25

                   X12                                             + X22                                  =       15

                                           X13                                    +      X23              =       10

X11, X12, X13, X21, X22. X23 >= 0  (greater or equal to 0)

1. Optimal solution using solver in excel:

• 5 units  have to be shipped from Jefferson city to Des Moines for a cost of $70
• 15 units have to be shipped from Jefferson City to Kansas for a cost of $135
• 10 units have to be shipped from Jefferson City  to St Louis for a cost of $10
• 20 units have to be shipped from Omaha to  Des Moines for a costo f $160
• 0 units Will be shipped from Omaha to Kansas City
• 0 units will be shipped from Omaha to St Louis

Following this combination, our optimal solution will lead us to a minimum total cost of $435

CHAPTER 6 PROBLEM 3

A.[pic 1]

500        10        400[pic 2][pic 3][pic 4]

[pic 5][pic 6][pic 7][pic 8]

        20[pic 9][pic 10]

        200

400                 12               15[pic 11]

        15

        18        300

B. Let us define our variables:

X11 = Quantity shipped from  Southern Gas to  Hamilton

X12 = Quantity shipped from  Southern gas to Butler

X13 = Quantity shipped from  Southern gas to Clermont

X21= Quantity shipped from  Northwest gas to Hamilton

X22= Quantity shipped from  Northwest gas to Butler

X23= Quantity shipped from  Northwest gas to Clermont

Objective function:

Min 10X11 + 20X12+ 15X12+12X21+15X22+18X23

Subject to:

X11       +   X12          +       X13                                                              <=    500

                                                             X21   +  X22    +       X23            <=     400

X11                                                 +   X21                                               =       400

...