warehouse in Milwaukee and another in Chicago. Because the company produces thousands of parts, it is considering an alternative strategy of locating a single, centralized warehouse between the two markets$$say$,$ in Kenosha, Wisconsin$-$that will serve all customer orders. Delivery time, referred to as lead time, from manufacturing to the warehouse$($s$)$ and ultimately to customers is unaffected by the new strategy.

Consider comparing a decentralized versus a centralized inventory system as it ultimately relates to the amount of safety stock $($extra inventory over and above mean demand$)$ held in the system.

Focus on one specific part: SurgeArrester. The lead time for this part from manufacturing to warehouses is one week. Suppose that the CEO of ElectroWorks requires a $99\%$ customer service level. This means that the probability of satisfying customer demand during the lead time is $0\mathrm{.}99.$ Assume that lead time demands for the Milwaukee warehouse, Chicago warehouse, and centralized warehouse are Normally distributed with the following means $\backslash$mu and standard deviations $\backslash$sigma :

$10$

$11$

$12$

$13$

$14$

$15$

$16$

$17$

$18$

$19$

$20$

$21$

Ready

$?$

X $=$ Milwaukee warehouse

Y $=$ Chicago warehouse

Correlation between X and Y

X $+$ Y $=$ centralized warehouse

MX $=415$ units My $=2689$ units P $=0\mathrm{.}52$ MX$+$Y$=3104$ units

ox $=48$ units Oy $=272$ units

OX$+$Y$=299\mathrm{.}78$ units

$($Use decimal notation. Use Table A$.$ Round your answer to the nearest integer.$)$

For a $99\%$ service level, how much safety stock of the SurgeArrester part does the