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colorado candy store orders its best-selling product, rocky chocolates, every 14 days. rocky chocolates have an average demand of 2,000 bags per day. the standard deviation of the daily demand was found to be 800 bags. it takes five days for the order to arrive. colorado candy would like to satisfy 99% of the demand. it is time to order, and they currently have 25.000 bags in stock. how many capsules should be ordered?

User Alchemical
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Final answer:

The store's reorder point (ROP) is 13,700 bags after considering the demand during the lead time and safety stock to cover 99% demand. With 25,000 bags in stock, they currently have more than enough to satisfy the ROP, and therefore do not need to order more chocolates at this time.

Step-by-step explanation:

The Colorado candy store needs to calculate how many bags of rocky chocolates should be ordered to meet the 99% demand by the time the next shipment arrives. To find this, we need to determine the reorder point (ROP), considering the lead time and the demand variability. The demand during the lead time (DLT) is the average demand per day multiplied by the lead time in days:

DLT = Average demand/day × Lead time days

DLT = 2,000 bags/day × 5 days

DLT = 10,000 bags

To cover 99% of the demand during the lead time, we apply the z-score for the 99% confidence interval, which is approximately 2.33 (from the standard normal distribution table), to the standard deviation and the square root of the lead time in days:

Safety stock = z × standard deviation × √(lead time days)

Safety stock = 2.33 × 800 bags × √(5 days)

Safety stock = 2.33 × 800 bags × 2.236

Safety stock ≈ 3,700 bags (rounded)

Therefore, the reorder point (ROP) is:

ROP = Demand during lead time + Safety stock

ROP = 10,000 bags + 3,700 bags

ROP = 13,700 bags

Since the store currently has 25,000 bags in stock, we subtract the ROP from the current inventory to determine how many bags need to be ordered:

Bags to be ordered = ROP - Current stock

Bags to be ordered = 13,700 bags - 25,000 bags

As the store already has more than enough stock to cover the ROP, no additional chocolates need to be ordered at this time.

User Mimicocotopus
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