Minimize the costs of shipping goods from factories to customers, while not exceeding the supply available from each factory and meeting the demand of each customer. Cost of shipping (\$ per product) Destinations Customer 1 Customer 2 Customer 3 Customer 4 Customer 5 Factory 1 \$1.75 \$2.25 \$1.50 \$2.00 \$1.50 Factory 2 \$2.00 \$2.50 \$2.50 \$1.50 \$1.00 Number of products shipped Customer 1 Customer 2 Customer 3 Customer 4 Customer 5 Total Capacity Factory 1 0 0 0 0 0 0 60,000 Factory 2 0 0 0 0 0 0 60,000 Total 0 0 0 0 0 Demand 30,000 23,000 15,000 32,000 16,000 Total cost of shipping \$0 Problem A company wants to minimize the cost of shipping a product from 2 different factories to 5 different customers. Each factory has a limited supply and each customer a certain demand. How should the company distribute the product? Solution 1) The variables are the number of products to ship from each factory to the customers. These are given the name Products_shipped in worksheet Transport1. 2) The logical constraint is Products_shipped >= 0 via the Assume Non-Negative option The other two constraints are Total_received >= Demand Total_shipped <= Capacity 3) The objective is to minimize cost. This is given the name Total_cost. Remarks This is a transportation problem in its simplest form. Still, this type of model is widely used to save many thousands of dollars each year. In worksheet Transport2 we will consider a 2-level transportation, and in worksheet Transport3 we expand this to a multi-product, 2-level transportation problem.