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Consider a manufacturing plant that employs 300 workers. The company starts the year with 500 units of inventory on hand. The forecast for demand for the next six months is 1,280, 640, 900, 1,200, 2,000, and 1,400. The plant would like to have an ending inventory of 600 units at the end of the six months. The cost of hiring one worker is $500 and the cost of firing a worker is $1000. Inventory is calculated based on the amount held at the end of each month and costs $80 per unit per month. All demand must be satisfied. The number of aggregate units produced by one worker in one day 0.14653. Assume that the number of working days in each month is 20.
1. Formulate a linear program to determine the company’s least total cost aggregate plan that can meet all of the demand without backlog.
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