TowAlong makes trailers at plants in Kansas City, Denver, and Raleigh, and ships these units to...
TowAlong makes trailers at plants in Kansas City, Denver, and Raleigh, and ships these units to distribution centers in Birmingham, Milwaukee, Los Angeles, and Seattle. In planning production for the next year, TowAlong estimates unit shipping cost between any plant and distribution center, plant capacities, and distribution center demands. These numbers are given in the table.
|
|
Distribution center |
||||
|
Plant |
Birmingham |
Milwaukee |
Los Angeles |
Seattle |
Capacity |
|
Kansas city |
$35 |
$40 |
$60 |
$120 |
12,000 |
|
Denver |
$30 |
$30 |
$45 |
$130 |
8,000 |
|
Raleigh |
$60 |
$65 |
$50 |
$100 |
5,000 |
|
Demand |
9,000 |
3,000 |
9,500 |
1,500 |
|
TowAlong faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, while not exceeding capacity and while meeting demand.
Solve for the optimal solution and the minimum total cost.
Please show excel and solver set-up. Thank you.
Homework Answers
Answer: Based on the given table, we tabulate the data in excel as shown below:
Since, total requirement < total capacity, the transportation problem is unbalanced problem. Hence, there will be one constraint in excel solver with "<=" sign
We find the optimum quantity of units transported from plant to distribution center to minimize total cost using excel solver as shown below:
The above table in form of formulas and excel solver extract is shown below for better understanding and reference:
The optimal solution is highlighted in green shown below. The total cost is highlighted in Orange in table below:
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