Big Time Tires manufactures heavy-duty truck tires. The tires are manufactured in St. Louis and Detroit and shipped to warehouses in Oakland, Miami, Minneapolis, Cleveland, and Boston. The following table shows the number of tires available at each plant, the number of tires required by each warehouse, and the shipping costs (in dollars per tire). a) Draw a network diagram of the problem. b) Is total supply and total demand equal to each other? c) Formulate a linear optimization model to determine the distribution plan that will minimize cost while meeting as much demand as possible. d) Use the Excel Solver to find the optimal distribution plan. Submit your Excel file (not a screen capture). e) What is the optimal distribution plan? f) What is the cost of the optimal distribution plan? g) Which warehouse will have a shortage and how big will the shortage be? Big Time Tires manufactures heavy-duty truck tires. The tires are manufactured in St. Louis and Detroit and shipped to warehouses in Oakland, Miami, Minneapolis, Cleveland, and Boston. The following table shows the number of tires available at each plant, the number of tires required by each warehouse, and the shipping costs (in dollars per tire). a) Draw a network diagram of the problem. b) Is total supply and total demand equal to each other? c) Formulate a linear optimization model to determine the distribution plan that will minimize cost while meeting as much demand as possible. d) Use the Excel Solver to find the optimal distribution plan. Submit your Excel file (not a screen capture). e) What is the optimal distribution plan? f) What is the cost of the optimal distribution plan? g) Which warehouse will have a shortage and how big will the shortage be