Imagine that you are running a clothing factory in a developing country. Your main product is a hand-maid handkerchief. You currently have 500 workers at the factory. Workers are required to work 26 days per month, 9 hours a day. Workers are paid $5 per hour. If a worker works more than 9 hours a day, the overtime portion will be paid at the rate of $6 per hour. Although there is no labour regulation, you do not want your workers to overwork and be tired out. You do not allow any worker to do overtime work more than 25 hours per month. On the average, one worker can make 12 handkerchiefs an hour. The fabric costs $1 per handkerchief. The inventory carrying cost is rather low. It costs $1 for 100 handkerchiefs per month. You began with only 500 units of handkerchiefs in stock at the beginning of fiscal year. You found it too low for the business. You want to have at least 2,000 units of handkerchiefs in stock at the end of the year. Solve the following aggregate planning problem: By using Linear Programming technique, formulate the aggregate planning problem for your factory, given a demand, Dt, in time period t (t = 1,12). Assume no backlogs, no subcontracting and no hiring/firing workers during the planning period. (10 marks) Revise the formulation if you can utilise a subcontractor to produce handkerchiefs at $1 for 5 units of handkerchiefs. Assume that the subcontractor can supply handkerchiefs up to 250 units per month.