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

COUNTRY EGYPT

(4)

UAE

(5)

Germany (1) $300 400 U.K. (2) 350 450 France (3) 250 300 The cost of transshipping a car in dollars from Egypt and the UAE to the three other countries are shown in the following table:

COUNTRY INDIA

(6)

SOUTH AFRICA

(7)

SINGAPORE

(8)

Egypt (4) 450 500 600 UAE (5) 400 350 550 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 by computer.