Final answer:
To manage complementary guest items such as soap and shampoo, it is recommended to order 17 bars of soap and set the reorder point at 19 bars. The total annual cost for this inventory system would be approximately $521.83.
Step-by-step explanation:
a. Recommend an order quantity and reorder point for this inventory system.
To determine the order quantity and reorder point, we need to calculate the safety stock level first.
Safety stock = (Z value for desired service level * standard deviation of demand * lead time) / square root of days in a year
For a 99.9% service level, the Z value is approximately 3.09. Using the given information, the safety stock = (3.09 * 3 * 7) / sqrt(365) = 0.97
Now, we can calculate the order quantity and reorder point:
Order quantity = mean demand + safety stock = 16 + 0.97 = 16.97 (rounded to 17 bars of soap)
Reorder point = mean demand + (Z value for desired service level * standard deviation of demand * sqrt(lead time)) = 16 + (3.09 * 3 * sqrt(7)) = 18.9 (rounded to 19 bars of soap)
b. What is the total annual cost for this inventory system?
The total annual cost can be calculated by multiplying the cost per order by the number of orders and adding it to the holding cost per bar of soap multiplied by the average inventory level:
Total annual cost = (cost per order * (365 / order frequency)) + (holding cost per bar * average inventory level)
From the given information, cost per order = $10, order frequency = 365 / 7 = 52.14, holding cost per bar = $0.05, and average inventory level = order quantity / 2 = 17 / 2 = 8.5.
Plugging in the values, the total annual cost = ($10 * 52.14) + ($0.05 * 8.5) = $521.4 + $0.425 = $521.825 (rounded to $521.83).