The Van Horne Company manufactures air conditioners that are sold to five large retail customers around the country. Van Horne is evaluating its manufacturing and logistics strategy to ensure that it is operating as efficiently as possible. The company can produce air conditioners at six plants and stock these units in any of four different warehouses. The cost of manufacturing and shipping a unit between each plant and warehouse is summarized in the following table along with the fixed operating cost and monthly capacity for operating each plant:

Similarly, the per-unit cost of shipping units from each warehouse to each customer is given in the following table, along with the monthly fixed cost of operating each warehouse:

The monthly demand from each customer is summarized below:

a. Considering all of the costs and demands tabulated above, what is the minimum monthly operating cost for Van Horne’s supply chain?
b. Which plants and warehouses should Van Horne operate to meet demand in the most cost-effective manner?

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Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Plant 6 WH1 WH 2 $700 $1,000 800 500 850 600 600 800 500 600 700 600 WH 3 WH 4 $900 $1,200 600 700 700 500 500 600 450 700 750 500 Fixed Plant Cost Capacity $55,000 40,000 45,000 50,000 42,000 40,000 300 200 300 250 350 400