A company has three laptop assembly plants running at full capacity in Des Moines, Racine, and Gary. These plants supply four distribution warehouses in St. Paul, Milwaukee, Chicago, and Detroit. The expected demand next year is forecast to exceed current capacity by 10 percent, so management plans to build another assembly plant. It has narrowed down the choice of sites to two possibilities: Kalamazoo and Duluth. The transportation costs, warehouse demands, and plant capacities are shown below: Quantity Produced per Year, units Plant Des Moines Racine Gary Kalamazoo Duluth 500 300 200 225 225 Plant Des Moines Racine Gary Shipment Costs, $ per Unit St. Paul 15 20 25 28 7 Warehouse Quantity Demanded per Year, units St. Paul Milwaukee Chicago Detroit Distribution Warehouses Milwaukee 20 3 8 11 12 Chicago 20 5 3 7 17 Detroit 30 20 13 6 11 225 175 325 350 Kalamazoo Duluth The company is very flexible as any plant can ship to any distribution warehouse. Assist the management in determining the location of the new plant. Explain why? Also provide the allocations.