PLE produces its most popular model of lawn tractor in its Kansas City and Santiago plants and

ships these units to major distribution centers in Atlanta, Caracas, Melbourne, Mexico City,

London, Shanghai, and Toronto. Unit shipping costs can be found in the PLE database. Both the

Kansas City and the Santiago plants have a maximum annual capacity of $60,000$ units. Longterm forecasts of annual demands at the distribution centers within $5$ years that PLE wants to

plan for are:

Distribution center Annual demand

Atlanta $60,000$

Caracas $10,000$

Melbourne $6,000$

Mexico City $4,000$

London $40,000$

Toronto $5,000$

Shanghai $50,000$

To support its growing sales, PLE is considering adding additional plants. The capacities of the

proposed plants and the fixed costs of construction can be found in the PLE database. If a new

plant is constructed, only one of the two potential capacities can be considered. Locations being

considered are Birmingham, Alabama; Singapore; Frankfurt, Germany; Mumbai, India; and

Auckland, New Zealand. Other options are to increase the capacities of the existing plants in

Kansas City and Santiago. Fixed costs of constructing new facilities or expanding the existing

plants can be found in the PLE database.

Develop and solve an optimization model to identify the best location for the new plants and

transportation allocations to meet demand. Some members of the executive committee are

concerned that the estimate for the China market $($demand at Shanghai$)$ is too uncertain and may

range from $20,000$ to $60,000$ units. In addition, it was suggested that the capacity of the Kansas

City plant be reduced to save distribution costs.

$2$

Write a report explaining your solution and any recommendations you may develop after

conducting appropriate sensitivity analyses with the model to address the concerns of the

executive committee.

Summarize your results in a well$-$written $2-3$ pages report