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Distribution System Design. The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: The shipping cost per unit from each plant to each distribution center is shown in the following Table. Shipping Cost per Unit(\$) for the Martin-Beck Distribution System a. Draw a network representation of the potential Martin-Beck distribution system. b. Develop a model for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. (Hint: use 0-1 variables to represent the plant construction decision). Solve your model in Excel with Solver