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1 A company must meet the following demands for a product: Month Demand January 30 February 30 March 20 Demand may be backlogged at a cost of $5 per unit per month. (That is, demand need not be satisfied on-time, but there is a penalty for delay.) Of course, all demand must be meet by the end of March. For example, if 1 unit of January demand is met during March, a backlogged cost of $5 X 2 = $10 is incurred. Monthly production capacity and unit production cost during each month are: Month January February March Production Unit Production Capacity Cost 35 $400 30 $420 34 $410 A holding cost of $20 per unit is assessed on the inventory at the end of each month a: Formulate a balanced transportation problem that could be used to determine how to minimize the total costs (including backlogging, holding, and produc tion costs) of meeting demand. (It is sufficient to display a transportation tableau with rows for sources and columns for destinations.) b: Use either Vogel's method or Northwest method to find a basic feasible solu- tion of the transportation problem. c: Use the transportation simplex method to determine how to meet each month's demand. Make sure to give an interpretation of your optimal solution. (For example, 20 units of second-month demand are met from first-month produc tion etc.) d: Formulate the production planning problem as a Linear Program and solve it using AMPL