Question

9. (2 Pts) Ruby owns a small café and uses a linen supplier for her tablecloths. Whenever she needs more tablecloths, she calls the supplier. She uses an average of 12 tablecloths a day with a standard deviation of 3 tablecloths. Lead time is a constant 2 days. If Ruby is willing to accept a 5% stockout risk, what is the reorder point, rounded to the nearest tablecloth? Assume demand is normally distributed. A. 28 B. 31 C. 34 D. 42

Answer 1

The correct answer is not provided among the given options.

To calculate the reorder point, we need to consider the lead time and the desired stockout risk.

The reorder point is the level at which Ruby should place an order to replenish her tablecloth inventory, so that she does not run out during the lead time.

First, let's calculate the average daily demand. Given that Ruby uses an average of 12 tablecloths a day with a standard deviation of 3 tablecloths, we know that the mean demand per day is 12 and the standard deviation is 3.

Next, we need to calculate the safety stock, which is the extra stock held to protect against stockouts during the lead time. To determine the safety stock, we need to find the z-score corresponding to the desired stockout risk. In this case, the stockout risk is 5%, so the z-score is 1.65 (from the standard normal distribution table).

The formula to calculate the safety stock is safety stock = z-score * standard deviation.
Therefore, the safety stock is 1.65 * 3 = 4.95 (rounded to the nearest tablecloth).

Finally, we can calculate the reorder point by adding the average daily demand to the safety stock.
Reorder point = average daily demand + safety stock
Reorder point = 12 + 4.95 = 16.95 (rounded to the nearest tablecloth).

Since we can't have a fraction of a tablecloth, we round the reorder point to the nearest whole number. Therefore, the rounded reorder point is 17 tablecloths.

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