A sports$-$car manufacturing company $$BTS$$ currently has warehouse in three locations, i$.$e$.,$Austin, Seattle, and Boston. The variance of weekly demands of all these cities and absolute value of the correlation co$-$efficient among these cities are given in Table $2.$ Also, it is known that demands of Austin and Seattle, and demands of Austin and Boston are positively correlated. In contrast, demands of Seattle and Boston are negatively correlated. The replenishment lead time for each of cities is $4$ weeks. Now, $$BTS$$ is considering to build a centralized warehouse in Seattle to reduce safety stock requirement. The Company maintains a customer service level of $0\mathrm{.}95.$Table $2.$ Description of the data related to demands and correlation co$-$efficient$$Variance of the weekly demand $($in weeks$)-$Austin$16$Variance of the weekly demand $($in weeks$)-$Seattle$25$Variance of the weekly demand $($in weeks$)-$Boston$36$Correlation between the demands of Austin and Seattle$0\mathrm{.}8$Correlation between the demands of Austin and Boston$0\mathrm{.}6$Correlation between the demands of Seattle and Boston$0\mathrm{.}4$Based on the information given above, answer the following questions$($a$)$What is the safety stock required for each of Austin, Seattle, and Boston? What is the totalsafety stock required for the decentralized option? $[2+2+2+2=8]($b$)$What is the standard deviation of the demand in case of centralized location in Seattle? Whatis the total safety stock required for the centralized option? $[2+2=4]($c$)$What is the reduction in the safety inventory if BTS moves from disaggregate to aggregateoption