Question 3 (30 points) WW manufactures automobiles in China, South Korea, and Japan and ships some of the automobiles directly to distributors in Arizona, Atlanta, and Kansas. The plants sometimes ship automobiles to factories in Costa Rica, Mexico, and Venezuela for final assembly because of tax advantage. Then the completed automobiles are sent to distributors in Arizona, Atlanta, and Kansas. The cost ($/unit) of direct shipment from East Asia plants to distributors, along with the supply of plants and demand of distributors are given in the following table: U.S. Distributor East Asia Plant 7. Arizona 8. Atlanta 9. Kansas Supply (1000s) 1. China $2900 3000 2000 4 2. South Korea 2600 2300 2700 6 3. Japan 2900 2900 3000 3.7 Demand 2.3 3.4 6 (1000s) The cost of shipment between East Asia Plants and Central America factories and between Central America factories and U.S. distributors are given below: East Asia Plant Factory 4. Costa Rica 5. Mexico 6. Venezuela 1. China $1200 1300 1100 2. South Korea 1600 1500 1300 3. Japan 1400 1300 1400 U.S. Distributor Factory 7. Arizona 8. Atlanta 9. Kansas 4. Costa Rica $900 700 800 5. Mexico 800 700 800 6. Venezuela 900 800 1000 a) (20 points) Formulate a linear programming model that will meet demand at the U.S. distributors at the minimum total cost. b) (10 points) Assume there is a fixed cost of $50000 for working with factory in Costa Rica. How would you incorporate this to your model? Explain clearly.