# A company has two manufacturing facilities, one in Atlanta and one in Los Angeles. The two…

A company has two manufacturing facilities, one in Atlanta and one in Los Angeles. The two facilities produce refrigerators and washer/dryers. The production capacities of these items in Atlanta are 5000 and 7000, respectively. Similarly, the capacity of the Los Angeles facility is 8000 refrigerators and 4000 washer/dryers. The company delivers these products to three major customers in New York City, Seattle, and Miami. The customer&#39;s demand is given below:

The items are transported from the manufacturing facilities to the customers via a railroad network. The unit transportation costs (no distinction is made between the two items) are summarized below. Also, because of limited space, the maximum number of refrigerators and/or washer/dryers that can be transported from a facility to a customer is given in the following table:

It is desired to find the shipping pattern that minimizes the total transportation cost.

a. Formulate the problem.

b. Use the Dantzig-Wolfe decomposition technique with two convexity constraints to solve the problem.

{Note: This problem is called a multicommodity transportation problem. The subproblem decomposes into two transportation problems. If you are familiar with the transportation algorithm, you can use it to solve the subproblems. Otherwise, use the simplex method to solve the subproblems.)

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