A manufacturing firm ships its finished products from three plants to three main distribution centers. The supply capacity of the plants, the demand for each warehouse and the transportation costs per ton are shown.
Supply Capacity for Plant 1 is 120. Supply Capacity for Plant 2 and Plant 3 is 80.
Demand for each warehouse: A = 150, B = 70, C = 60
Plant 1 transportation costs: Warehouse A = $8,Warehouse B = $5,Warehouse C = $6
Plant 2 transportation costs: Warehouse A = $15, Warehouse B = $10, Warehouse C = $6
Plant 3 transporation costs: Warehouse A = $3, Warehouse B = $9, Warehouse C = $10
a. What is the optimal amount from each plant to a corresponding Warehouse?
b. What is the optimal cost?