The demand for a certain manufactured product during the next four months is expected to be 400, 300, 200, and 450 units respectively. The cost of manufacturing with regular, overtime and subcontracting options and the capacities are given below: Regular Production Overtime Production Subcontract Production Manufacturing Cost Capacity/month 300 100 100 40 60 90 The carrying cost is $5 per month/unit. No backorders allowed. (a) Set this up as a transportation problem and find the initial basic feasible solution using North-West Corner rule. (5 points) (b) Make sure that there is appropriate number of filled cells. How many filled cells are there? (5 points) (c) What is the total cost at this stage? (5 points)