2. A bicycle manufacturer is determining its production schedule for the next 3 months. Assume that it costs this company $150 to manufacture each bicycle. At the end of each month, a holding cost of $25 per bicycle left in inventory is incurred. No more than 40 bicycles can be stored in inventory at any point in time. Monthly demands for bicycles are projected to be as follows: 150 in month 1; 175 in month 2;165 in month 3. Assume that at the beginning of month 1, 10 completed bicycles are in inventory. Finally, this company can produce up to 170 bicycles per month. a) Formulate a linear programming (LP) model to find a cost-minimizing production schedule that meets all demands on time. Note: Clearly define your notation. b) Model the problem in Excel and solve it using Excel Solver. c) Model and solve the same problem using Gurobi, using the Excel file in b) as the input data file. Write your solution to a new sheet of the same Excel file and rename the sheet as "Solution_Gurobi." Properly name your column headers and row labels (if any) and make sure that your solution is readable