A car manufacturer has production plants in Germany, the United Kingdom, and France, and it exports cars to several other countries. The manufacturer’s supply chain includes manufacturers, distributors, and retailers. The plant in Germany wants to export 5,000 cars; the plant in the UK, 2,500 cars; and the plant in France, 3,000 cars. The demand for cars from India is at least 2,000 cars; South Africa, 4,000 cars; and Singapore, 1,000 cars. Cars are first exported to the distributors in Egypt and the UAE and they in turn export cars to the retailers’ countries. Cars are not shipped directly from the plants to retailers. Distributors do not stock cars; they export whatever they receive from the manufacturers. Since the custom rules and currency rates are different in these countries, the transportation cost per car need not depend on the distance between these locations. The following table shows the transportation cost in dollars to ship a car between locations.

The cars are transshipped from Egypt and the UAE to three other countries as shown in the following table.

The manufacturer wants to determine the export mix of cars that will minimize transportation cost.
a. Formulate a linear programming model to this problem.
b. Solve this model using computer.

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Country Germany (1) UK(2) France (3) Egypt (4) 300 350 250 UAE (5) 400 450 300