The Scott Manufacturing Company (SMC) operates two plants, one in Bolton with an annual capacity of 21650 units and other in Georgetown with annual capacity of 12850 units. Product is shipped to regional distribution centers located in DC-A, DC-B, and DC-C. Because of an anticipated increase in demand, SMC plans to increase capacity by constructing new plant/s in one or more of the following cities: City-A, City-B, or City-C. The estimated annual fixed cost and the annual capacity for the three proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity (Units) City-A $217500 16520 City-B $306250 22345 City-C $347190 27765 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Centers Annual Demand (Units) DC-A 21625 DC-B 23780 DC-C 20920 The shipping costs per units from each plant to each distribution center are as follows: Plant Site Distribution Centers DC-A DC-B DC-C Bolton $8 $7 $5 Georgetown S7 $5 $6 City-A $9 $4 $5 City-B $6 $9 $4 City-C $11 $3 $6 Your task is to assist in the formulation of the problem as a linear programming model for choosing the best plant location/s to meet the anticipated demand at the distribution centers with the minimum total cost and for determining how much to ship from each plant to each distribution center. Specifically, answer the following questions: (a) Clearly define all decision variables. (b) Clearly formulate the objective function. (c) Clearly specify all the constraints such that only constants (value) appear on the right-hand sides of the constraints