Question: A manager has prepared a forecast of expected aggregate demand for the next six months. Develop an aggregate plan to meet this demand given this additional information: A level production rate of 100 units per month will be used. Back orders are allowed, and they are charged at the rate of $8 per unit per month. Inventory holding costs are $1 per unit perA manager has prepared a forecast of expected aggregate demand for the next six months. Develop an aggregate plan to meet this demand given this additional information: A level production rate of 100 units per month will be used. Back orders are allowed, and they are charged at the rate of $8 per unit per month. Inventory holding costs are $1 per unit per month in ending inventory. Determine the cost of this plan if regular time cost is $20 per unit and beginning inventory is zero.Month Forecast1 802 1003 1204 1105 1006 90

The question is asking for an aggregate plan to meet the forecasted demand over the next six months, given certain conditions. Here's how to approach this:

Step 1: Identify the forecasted demand for each month. From the question, we have:

Month 1: 80 units Month 2: 100 units Month 3: 120 units Month 4: 110 units Month 5: 100 units Month 6: 90 units

Step 2: Determine the production rate. The question states that a level production rate of 100 units per month will be used. This means that the company will produce 100 units every month, regardless of the demand.

Step 3: Calculate the inventory or backlog for each month. If the production is less than the demand, there will be a backlog. If the production is more than the demand, there will be an inventory.

Step 4: Calculate the cost for each month. The cost includes the production cost, the inventory holding cost, and the backlog cost. The production cost is $20 per unit. The inventory holding cost is$1 per unit per month. The backlog cost is $8 per unit per month.

Step 5: Sum up the costs for all the months to get the total cost of the plan.

Let's calculate:

Month 1: Production = 100 units Demand = 80 units Inventory = 20 units Cost = (100 units * $20/unit) + (20 units *$1/unit) = $2020

Month 2: Production = 100 units Demand = 100 units Inventory = 20 units (from previous month) Cost = (100 units * $20/unit) + (20 units *$1/unit) = $2020

Month 3: Production = 100 units Demand = 120 units Backlog = 20 units Cost = (100 units * $20/unit) + (20 units *$8/unit) = $2160

Month 4: Production = 100 units Demand = 110 units Backlog = 30 units (10 units added to previous month's backlog) Cost = (100 units * $20/unit) + (30 units *$8/unit) = $2240

Month 5: Production = 100 units Demand = 100 units Backlog = 30 units (no change from previous month) Cost = (100 units * $20/unit) + (30 units *$8/unit) = $2240

Month 6: Production = 100 units Demand = 90 units Inventory = 10 units (backlog of 30 units is reduced by 20 units) Cost = (100 units * $20/unit) + (10 units *$1/unit) = $2010

Total cost of the plan = $2020 +$2020 + $2160 +$2240 + $2240 +$2010 = $12690.