[Question 4] (The total marks available for this question is 20. The weighting of each subpart is indicated in %.) A company must meet the following demands for a product: January, 30 units; February, 30 units; March 20 units. Demands can be backlogged at a cost of 5 per unit per month. All demands must be met by the end of March. Thus if 1 unit of January demand is met during March, a backlogging cost of 10 (= 5 x 2) is incurred. Monthly product capacity and unit production cost during each month are given in the following table. A holding cost of 20 per unit is assessed on the inventory at the end of each month. Production capacity Unit production cost Month January 35 400 February 30 420 March 35 410 (a) Formulate a balanced transportation problem that can be used to determine how to minimise the total cost (including backlogging, holding, and production costs) of meeting demand. Provide all details of your formulation, including all unit costs in tabular form with all supply and demand points. [40% ] (b) Use the northwest corner method to find a basic feasible solution. Provide an interpretation of the basic feasible solution in terms of the original problem. What is the total cost of this basic feasible solution? [20%] (c) Use the transportation simplex method (without using Excel) to determine how to meet the demand of each month optimally. Provide all working details. Make sure to give an interpretation of your optimal solution. What is the total cost of your optimal solution? [40%]