A manufacturer of heavy truck engines must develop an aggregate production plan, given the following demand forecasts for engines. The company currently has 13 workers and makes 130 engines per month. Regular labour cost is $500 per engine. The beginning inventory is zero. Overtime labour costs $750 per engine. Hiring cost is $3,000 per worker. Inventory holding cost is $50 per engine per month, and back-order cost is $250 per engine per month.
Develop the minimum cost plan for this company.

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Month 1 2 3 4 5 6 7 8 Total Forecast 120 135 140 120 125 125 140 135 1,040