Question: Multi-period production and inventory planning models determine a production schedule and ending inventory schedule for each of several periods that will maximize profit or minimize cost. Considering selling price, regular production costs, overtime costs, inventory carrying costs, and lost sales costs, develop a three-period production and inventory planning model for Allen Manufacturing company. Use the following relevant information.

Period Selling Price Production Cost Demand Inventory Holding cost

1 $5.00 $2.80 500 $.50

2 $5.20 $2.90 300 $.50

3 $5.50 $3.00 400 $.55

Production Capacity

Period Regular Overtime

1 250 100

2 300 100

3 300 125

The overtime cost per unit in each period is 20% greater than the production cost per unit shown. The lost sales cost, which is $4 per unit in any period, accounts for lost customer goodwill, but does not account for the cost associated with the lost revenue. The beginning inventory for the period 1 is 100 units. In addition, the firm wants to have at least 50 units in ending inventory for period 3 to prepare for period 4. Develop a linear program that can be used to determine the optimal production and inventory schedule for Allen Manufacturing. Determine the sales, regular production, overtime production, ending inventory, and lost sales for each of the three periods. What is the net profit associated with your solution?

Price: $2.99

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