Steinwelt piano manufactures uprights and consoles in two plants, plant i and plant ii. the output of plant i is at most 300/month, and the output of plant ii is at most 250/month. these 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 pianos/month, warehouse b requires at least 150 pianos/month, and warehouse c requires at least 200 pianos/month. the shipping cost of each piano from plant i to warehouse a, warehouse b, and warehouse c is $30, $30, and $40, respectively, and the shipping cost of each piano from plant ii to warehouse a, warehouse b, and warehouse c is $40, $35, and $25, respectively. what shipping schedule will enable steinwelt to meet the requirements of the warehouses while keeping its shipping costs to a minimum?