The store currently is using a fixed period system to manage inventory. A staff checks inventory of each distinct item once every $10$ days. A particular cooking wok imported from the Netherlands is priced at $$220$ per unit. The annual holding cost per unit is $15\%$ of the product price. The daily demand for the cooking wok follows a normal distribution with a mean of is $5$ units and standard deviation of $2$ units. When the shop places a new order of the cooking wok, it takes the supplier $8$ days to fulfill the order.

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$1.$ What is the target inventory level of the cooking wok if the store would like to tolerate $1\%$ chance of having a stockout?

The target inventory level is approximately Question Blank $1$ of $4$

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$2.$ What is the safety stock annual holding cost when using the fixed period inventory control system?

The safety stock annual holding cost is $Question Blank $2$ of $4$

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$3.$ To save money, the store manager is thinking about switching to a real$-$time inventory system $($i$.$e$.$ fixed quantity inventory control system$).$ In order to use the real$-$time inventory system, the store needs to acquire an inventory information system from a vendor, at the cost of $$2,000$ per year. Is it worth switching to the fixed quantity system? Perform relevant calculations to justify.$$

My answer to this question is$($Yes or No$)$ Question Blank $3$ of $4,$ here is why Question Blank $4$ of $4.$