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Gang Aft Agley, a manufacturing company, faces the aggregate planning problem for two products. Consultation with customers has indicated a demand forecast for each product over the next 6 months to be as shown in table below. For product 1, cost of regular production is $5 per unit, the cost of producing the same unit on overtime is $7.50, the cost of subcontracting is $9 per unit. For product 2, cost of regular production is $7 per unit, the cost of producing the same unit on overtime is $10, the cost of subcontracting is $12 per unit. The plant currently maintains 400 product 1 and 500 product 2 in inventory. The cost of holding both products in inventory is $2 per month. The labor contract at the plant prohibits both overtime and subcontracting (both products together) output to exceed 600 units in any six month window. The plant capacity is 900 (both products together) units per month produced using two shifts, regardless of the number of days in a month. Note: Provide a model formulation for part a and solution in Excel for all parts on seperate sheets. a. Assuming no backlogs, what is the optimum production schedule for Gang Aft Agley? What is the annual cost of this schedule? What inventories does the optimal production schedule build? Does this seem reasonable? b. Is there any value for management to negotiate an increase of allowed production in overtime from 600 to 800? What variables are affected by this change? c. Is there any value for management to increase the capacity from 900 to 1000 units allowed production in overtime remains 600)? What variables are affected by this change? Is this better than the change from part b? Month Product 1 Demand Product 2 Demand Jan 400 600 Feb 600 400 Mar 600 500 Apr 500 500 May 800 600 Jun 700 900