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Steinwelt Piano manufactures uprights and consoles in two plants, Plant 1 and plant 2. the output of plant 1 is at most 300/month, and the out put of plant 2 is at most 250/month. theses pianos are shipped to three warehouses that serve as distribution centers for Steinwelt. To fill current and projected future orders,Warehouse A requires a minimum of 200 piano/nibtm Warehouse B requires at least 150 pianos/month, and Wrehouse C requires at least 200 pianos/month. The shipping cost of each piano from Plant 1 to Warehouse A, Warehouse B, and Warehouse C is $60, $60, and $80, respectively, and the shipping cost of each piano from Plant 2 to Warehouse A, Warehouse B, and Warehouse C is $80, $70, and $50, repectively. What shipping schedule will enable Steinwelt to meet the requirements of the warehouses while keeping the shipping costs to a minimum? What is the minimum cost?
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Shipping Schedule: Plant 1: 200 pianos to Warehouse A, 100 pianos to Warehouse B Plant 2: 50 pianos to Warehouse B, 200 pianos to Warehouse C Minimum Cost: $20,220. This shipping schedule satisfies the requirements of all three warehouses while also minimizing the shipping costs. The total cost of shipping is as follows: Plant 1 to Warehouse A - 200 pianos x $60 = $12,000, Plant 1 to Warehouse B - 100 pianos x $60 = $6,000, Plant 2 to Warehouse B - 50 pianos x $80 = $4,000, Plant 2 to Warehouse C - 200 pianos x $50 = $10,000 = Total cost of $20,220.
