A manufacturer is considering alternatives for building new plants, to be located closer to three of its primary customers with whom it intends to develop long-term, sole-supplier relationships. The net cost of manufacturing and transporting each unit of the product to its customers will vary depending on where the plant is built and the production capacity of the plant. These costs are summarized in the table below:

The annual demand for products from customers X, Y, and Z is expected to be 40,000, 25,000, and 35,000 units, respectively. The annual production capacity and construction costs for each plant are:

The company wants to determine which plant to build to satisfy customer demand at a minimum total cost.
a. Formulate an ILP model for this problem.
b. Create a spreadsheet model for this problem and solve it.
c. What is the optimalsolution?

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Net Cost per Unit to Supply Customer X 35 30 45 45 40 50 Plant 3 70 65 50 20 45 25 65 45 45 Plant Production Capacity 40,000 30,000 50,000 20,000 40,000 Construction Cost (in $1000s) $1,325 $1,100 $1,500 $1,200 $1,400 4 5