ABC Company, a manufacturer of roofing supplies, has developed monthly forecasts for roofing tiles. The forecasted demand and the expected production days for months March to August in 2013 are given below: Month Forecasted demand (units) Production days March 2400 23 April 4500 20 May 2600 22 June 7000 20 July 2000 23 August 3000 22 ABC works 8 regular hours in each working day and past experience shows that one worker takes 1 hour to produce one tile. The company has estimated that there would be 5 production workers working in February 2013 and 250 tiles in inventory at the end of February 2013. Labor Union restricts ABC that overtime hours cannot exceed 20% of straight time (regular) hours in each month. ABC wants to keep at least 200 tiles in inventory at the end of August 2013. ABC has the following cost information: Inventory holding cost = $3/unit/month Backorder cost = $10/unit Subcontracting cost = $30/unit Straight time labour cost = $12/hour Overtime cost = $24/hour Hiring cost = $800 Firing cost = $1600 If ABC allows backorders but does not want to use subcontracting or overtime: a. Find the minimum constant workforce required to meet the above requirement (level production strategy). b. Develop an aggregate production plan with the minimum constant workforce obtained in part (a) (level production strategy). c. Estimate the total cost of the plan in (b). If ABC wants to maintain zero inventory at the end of each month except for August, and does not want to use subcontracting or overtime, d. Develop an aggregate production plan with zero inventory policy (chase strategy with flexible working hours). e. Estimate the total cost of the plan in (d)