Nash Auto has two plants, two warehouses, and three customers. The plants are in Detroit and Atlanta, the warehouses are in Denver and New York, and the customers are in Los Angeles, Chicago, and Philadelphia.

Cars are produced at plants, then shipped to warehouses, and finally shipped to customers. Detroit can produce 200 cars per week, and Atlanta can produce 160 cars per week. Los Angeles requires 80 cars per week, Chicago requires 70, and Philadelphia requires 60.

It costs $8,000 to produce a car at each plant. The costs of shipping a car between various cities are listed in the table. Assume that during a week, at most 75 cars can be shipped from a warehouse to any particular city.

(A) Determine how to meet Nash's weekly demands at minimum cost.

(B) Note the total cost.

C) Solve the same problem but now set production cost in Detroit at $9,000 per unit and Atlanta at $7,000 per unit. Present the same documentation of your solution as above. Do these revised production costs change the pattern of shipments? If so, comment on why different routes are used.

(D) Return to the original problem. Increase weekly capacity at the Detroit plant in increments of 20 cars/week. Explain what happens to shipments as Detroit capacity increases.

(E) Return to the original problem. Assume Nash's agent in China has acquired the necessary permits and will sell Nash autos in China. Initial demand is 80 cars/week, shipped from L.A.

How will this demand be met? Increase capacity as described above, and explain what happens to shipments as a result.

Alternatively, increase outbound capacity from warehouses in increments of 20 cars per week. What happens to shipments? Would you prefer to increase production capacity in Detroit or shipping capacity?