### Identify the new plant locations and the minimum cost

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The annual fixed cost, the cost of production and the plant capacity for each of the ten plant locations (A thru J) is shown in Table 1.

The distance in miles between the ten potential plants and the six markets (1 thru 6) is given in Table 2. Table 2 also shows the demand for the soft drink at the six markets.

ESDB uses trucks for transporting the soft drink from the bottling plant to the different markets. These trucks have a capacity of 150 hectoliters and incur an operating cost of \$0.92 per mile. After delivery to the market, the trucks return empty to the plant.

1) Formulate an integer linear programming model to minimize the total cost for the supply chain network and to determine the number of plants to be opened and the locations of these plants. Make sure you clearly define the decision variables, the objective function and the constraints of your model.

2) Use the Solver functionality in Excel to solve the model. What are the locations for the open plants and what is the optimal total cost of the network? Are all open plants being used to full capacity? Which, if any plant has excess capacity and what is the excess capacity available at this plant?

3) Suppose that the maximum distance between a plant and a market cannot exceed 150 miles. What additional decision variables and/or constraints do you need to add to your model in question 1) to accommodate this condition?

4) Resolve the model developed in 3) and identify the new plant locations and the minimum cost.

5) Identify an additional scenario and develop a model for the scenario. Analyze the model and discuss your model results.

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