Final answer:
To meet the demand for the next 5 months, we need to develop an aggregate plan based on a level production rate of 50 units per month. By calculating the production, backorder, and inventory levels for each month, we can determine the total cost. The total cost for all 5 months is $6,450.
Step-by-step explanation:
To develop an aggregate plan that meets demand, we need to calculate the production, backorder, and inventory levels for each month. Let's start by calculating the total demand for each month. Month 1 has a demand of 40 units, month 2 has a demand of 50 units, month 3 has a demand of 60 units, month 4 has a demand of 60 units, and month 5 has a demand of 40 units.
Based on a level production rate of 50 units per month, we can produce 50 units in months 1-5. Any excess demand will result in backorders. The number of backorders allowed is 31 units per month, and each backorder costs $15 per unit per month.
To calculate the total cost, we need to consider the production costs, backorder costs, and inventory holding costs. The production cost is $25 per unit. The backorder cost is $15 per unit per month, and the inventory holding cost is $2 per unit per month. The total cost can be calculated using the formula: Total Cost = Production Cost + Backorder Cost + Inventory Holding Cost.
Let's calculate the total cost for each month:
Month 1: Total Cost = (50 * $25) + (0 * $15) + (10 * $2) = $1,250
Month 2: Total Cost = (50 * $25) + (0 * $15) + (0 * $2) = $1,250
Month 3: Total Cost = (50 * $25) + (0 * $15) + (20 * $2) = $1,350
Month 4: Total Cost = (50 * $25) + (0 * $15) + (20 * $2) = $1,350
Month 5: Total Cost = (50 * $25) + (0 * $15) + (0 * $2) = $1,250
The total cost for all 5 months is $6,450. Therefore, the correct answer is C. $6,440.