Could you please answer the attached question $?$ Consider $N$ retailers which order a common item. Let ${}_i$ be the deter$-$

ministic demand rate for the item at retailer $i.$ The unit purchasing cost and the

holding cost rate of the item is the same for all retailers $(c$ and $h,$ respectively$).$ Let

$k$ be the fixed order cost for the item at retailer $i($again$,$ same at all warehouses$).$

Assume also that no planned backorders are allowed. In summary, each retailer

operates in an EOQ environment. Let's call this system "the decentralised model"

$($DM$).$ An alternative mode of operation is to centralise the ordering decision of

the retailers. A central decision making unit will order a consolidated quantity for

all retailers, considering the total demand $={\displaystyle \underset{i=1}{\overset{N}{}}}{}_i.$ The fixed ordering cost for

the consolidated system is $K=k$ where $>0.$ We call the second system as

$"$ the centralised model" $($CM$).$

a$.$ Find the range of $$ values for which $CM$ always performs better

than DM$.$

b$.$ For $N=2$ discuss that the performance of $CM$ become similar

better as the warehouses become more symmetric $({}_1$ and ${}_2$ become similar$).$