2 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 ofan 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 estimatedannual fixed cost and the annual capacity for the four proposed plants are as follows:Plant NumberProposed Plant Annual Fixed Cost Annual CapacityDetroit$200,00010,0002Toledo$275,00020,000Denver$350,00030,0004Kansas City$525,00040,000The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows.DistributionCenter NumberDistributionAnnual DemandCenter1.Boston20,0002Atlanta30,0003Houston30,000The shipping cost per unit from each plant to each distribution center is as follows.Distribution CentersPlant Site Boston Atlanta HoustonDetroitToledo44Denver7Kansas City1042St. Louis843 (a) Formulate a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand and minimize total cost(in thousands of dollars). (Let x = units shipped in thousands from plant i to distribution center j with the existing plant in St. Louis being plant number 5. Let y, = 1 if a plant is constructed inDetroit and 0 if not, y, = 1 if a plant is constructed in Toledo and 0 if not, y, = 1 if a plant is constructed in Denver and O if not, and y. = 1 if a plant is constructed in Kansas City and O if not.)Mins.t.Detroit CapacityToledo CapacityDenver CapacityKansas City CapacitySt. Louis CapacityBoston DemandAtlanta DemandHouston DemandXy 2 0 for all i and j and y,, y2, Y3, Y4 binary(b) Solve the model you formulated in part (a). What is the optimal cost (in $)?What is the optimal set of plants to open? (Select all that apply.)O DetroitO ToledoO DenverO Kansas City

Given Information: The shipping cost per unit from each plant to each distribution center is as…

(a) Formulate (in thousands of dollars). (Let x = units shipped in thousands from plant i to distribution center j with the existing plant in St. Louis being plant number 5. Let y, = 1 if a plant is constructed in Detroit and 0 if not, y, = 1 if a plant is constructed in Toledo and o if not, y, = 1 if a plant is constructed in Denver and O if not, and y, = 1 if a plant is constructed in Kansas City and O if not.) mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand and minimize total cost Min s.t. Detroit Capacity Toledo Capacity Denver Capacity Kansas City Capacity St. Louis Capacity Boston Demand Atlanta Demand Houston Demand X 2 0 for all i and j and y, Y2, Y3, Y4 binary