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?

Question

Mathematics

Kamden Estrada

19 January, 14:36

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?

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Isabela Stuart · Answer 1

You can write the equations necessary to solve this by linear programming, or you can just think about it a bit.

The cheapest shipping is from Plant II to Warehouse C, so the entire stock required by Warehouse C should come from Plant II, 200 pianos.

The next cheapest shipping from Plant II is to Warehouse B, so the remaining 50 pianos produced at Plant II should go there.

Then the pianos from Plant I need to fill the rest of the need, so will be allocated as 200 pianos to Warehouse A and 100 to Warehouse B.

In summary, the schedule is

... I → A: 200 pianos

... I → B: 100 pianos

... II → B: 50 pianos

... II → C: 200 pianos