Problem Text A fruit importer faces the weekly problem of meeting demand for bananas at three regional customer centers (Denver, Kansas City, and Fort Worth) from the supply available at the source countries: Honduras and Costa Rica. Bananas are shipped from the sources, to two port facilities at Miami and San Diego. Miami is also a regional customer center. See the network diagram below. Supplies and demands (in hundreds of pounds) for the coming week are shown in the tables below. Transportation costs are roughly proportional to the

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem Text A fruit importer faces the weekly problem of meeting demand for bananas at three regional customer centers (Denver, Kansas City, and Fort Worth) from the supply available at the source countries: Honduras and Costa Rica. Bananas are shipped from the sources, to two port facilities at Miami and San Diego. Miami is also a regional customer center. See the network diagram below. Supplies and demands (in hundreds of pounds) for the coming week are shown in the tables below. Transportation costs are roughly proportional to the amount of bananas and the distance the product must be shipped. The number of miles (in hundreds) between locations is given in the next two tables. That is, treat these values as the unit costs for the problem. Source Supply (lbs.x100) 1. Honduras 200 2. Costa Rica 100 Customer Demand (lbs.x100) 3. Miami 70 5. Denver 80 6. Kansas City 60 7. Fort Worth 85 Distance from Source to Port (miles x 100) 3. Miami 4. San Diego 1. Honduras 9 18 2. Costa Rica 12 20 Distance from Port to Customer (miles x 100) 5. Denver 6. Kansas City 7. Fort Worth 3. Miami 21 12 13.5 4. San Diego 11 18 13.5 Anything shipped into a port must be shipped out to a customer (treat Miami as essentially both a port and a customer). How should the bananas be transported to minimize total “cost” (banana-miles)? Two spreadsheet templates are provided for the problem. One is in standard form, and one is in the alternate form (see the transshipment problem from class/Canvas).

Expert Solution
Step 1: Linear programming problem

To minimize the total cost (banana-miles) while meeting the demand for bananas at the three regional customer centers (Denver, Kansas City, and Fort Worth) from the supply available in Honduras and Costa Rica, you can use a transportation model or linear programming. Here's a high-level approach:

  1. Define Decision Variables:

    • Let Xij be the number of hundred pounds of bananas transported from source i (Honduras or Costa Rica) to destination j (Miami, San Diego, Denver, Kansas City, or Fort Worth).
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