(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