Sales forecasts for a certain product for the first 6 months of 2012 are given in the following:

Production can be increased from 1 month to the next at a cost of $5 per unit, by hiring new workers. Production can also be decreased at a cost of $3 per unit by laying off existing workers. Inventory is limited to 7000 units due to warehouse capacity. Storage cost is estimated at $3 per unit per month based on the end of the month inventory. December 2011 production is set at 2000 units and the expected inventory at the end of December 2011 is 1000 units. The company does not allow shortages and the demands must be met every month. The company would like to have an inventory of 3000 units at the end of June 2012. The problem is to determine the production schedule for the first 6 months of 2012 that will minimize the total cost of production changeovers and storage. Formulate this as a LP problem as follows:

(a) Define your variables clearly.

(b) Write out the linear constraints that must be satisfied, briefly explaining the significance of each.

(c) Write out the linear objective function that must be minimized.