Assignment $5--$Warehouse Centralization Problem

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 centralized and keep the same customer service level, determine the average warehouse inventory levels, using the number of warehouses below and the square root rule. The square root rule can be found in Chapter $9$ on page $405$ if using a looseleaf copy of the textbook. If using the online Cengage textbook, you will find the square root rule in section $9-3$b: "Risk Pooling and Warehouse Location" toward the bottom of the page. You will need the square root calculator to complete this problem. $($Most cell phone calculators have this$--$you may have to turn the phone sideways to see it on your calculator$).$ Even if you do not have the correct answer, partial credit will be awarded for showing your work.

a$)$ Three warehouses

b$)$ One warehouse

c$)$ What is the percentage reduction in system inventory for the two systems above, compared to the original system?