A current warehouse system has six warehouses with $3,000$ units at each warehouse. If the company desires to change the number of warehouses to become more decentralized and keep the same customer service level, determine the average warehouse inventory levels, using the number of warehouses below and the square root rule.

a$)$ nine warehouses

b$)$ twelve warehouses

Answer using the formula on the image $($square$-$root rule$)$

$S_2=\frac{\sqrt[\phantom{2}]{N_2}}{\sqrt[\phantom{2}]{N_1}}*(S_1)$

Where: $,S_1=$ Total system stock for the N$1$ warehouses

$S_2=$ Total system stock for the N$2$ warehouses

$N_1=$# of warehouses in the existing system, &

$N_2=$# of warehouses in the proposed system