Final answer:
The annual ordering cost is $85.71. The annual carrying cost is $13,200. The total cost is $13,285.71. A new order should be placed. The amount of units that should be ordered is 980 units.
Step-by-step explanation:
The annual ordering cost can be calculated by dividing the total demand rate by the production rate, and then multiplying it by the ordering cost per order.
In this case, the annual ordering cost is (20 units/day ÷ 70 units/day) × $300/order = $85.71.
The annual carrying cost can be calculated by multiplying the average inventory level by the carrying cost per unit.
In this case, the average inventory level is the sum of the safety stock, stock on-hand, and total open orders, which is 120 units + 300 units + 900 units = 1320 units.
Therefore, the annual carrying cost is 1320 units × $10/year = $13,200.
The total cost can be calculated by adding the annual ordering cost and the annual carrying cost.
In this case, the total cost is $85.71 + $13,200 = $13,285.71.
A new order should be placed if the stock on-hand plus safety stock is less than the reorder point. The reorder point can be calculated by multiplying the demand rate by the supply lead time.
In this case, the reorder point is 20 units/day × 7 days/week × 10 weeks = 1400 units.
Since the stock on-hand plus safety stock is 300 units + 120 units = 420 units, which is less than the reorder point, a new order should be placed.
The amount of units that should be ordered can be calculated by subtracting the stock on-hand plus safety stock from the reorder point.
In this case, the amount of units that should be ordered is 1400 units - 420 units = 980 units.