A company is considering centralizing inventory from two locations to one location for Item X$.$ At Location $1,$ Item X has an average demand of $15$ units a day and a standard deviation of demand of $4$ unit a day. At Location $2,$ Item X has an average demand of $35$ units a day and a standard deviation of demand of $4\mathrm{.}2$ units a day. The correlation of demand of Item X between Location $1$ and Location $2$ is $0\mathrm{.}50.$ Assume demand at both locations is approximately normal. If an analyst uses the square root law to approximate the percentage reduction in safety stock from centralizing this item, which will happen?

Question $9$ options:

a$)$

The square root law will be an accurate representation of the safety stock reduction from centralizing inventory.

b$)$

The square root law will understate the safety stock reduction from centralizing inventory.$$

c$)$

The square root law will overstate the safety stock reduction from centralizing inventory.$$