A current warehouse system has eight warehouses with $5,000$ units at each warehouse.

a$.$ 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 level, using twelve warehouses and the square root rule. Do not round intermediate calculations.

Round your answer to the nearest whole number.

units

b$.$ 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 level, using sixteen warehouses and the square root rule. Do not round intermediate calculations.

Round your answer to the nearest whole number.

units

c$.$ What is the percentage increase in system inventory for the two systems above, compared to the original system? Do not round intermediate

calculations. Round your answers to two decimal places.

$12$ warehouses vs$.8$ warehouses:

$\%$

$16$ warehouses vs$.8$ warehouses:

$\%$