3 A company must meet the following demands for a product: January, 30 units; February, 30 units; March, 20 units. Demand may be backlogged at a cost of

$5/unit/month. All demand must be met by the end of March.

Thus, if 1 unit of January demand is met during March, a backlogging cost of 5(2)  $10 is incurred. Monthly production capacity and unit production cost during each month are given in Table 66. A holding cost of $20/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 cost (including backlogging, holding, and production costs) of meeting demand.

b Use Vogel’s method to find a basic feasible solution.

c Use the transportation simplex to determine how to meet each month’s demand. Make sure to give an interpretation of your optimal solution (for example, 20 units of month 2 demand is met from month 1 production).