Cloud Services Capacity Planning. Galaxy Cloud Services operates several data

centers across the United States containing servers that store and process the data

on the Internet. Suppose that Galaxy Cloud Services currently has five outdated data

centers: one each in Michigan, Ohio, and California and two in New York.

Management is considering increasing the capacity of these data centers to keep up

with increasing demand. Each data center contains servers that are dedicated to

Secure data and to Super Secure data. The cost to update each data center and the

resulting increase in server capacity for each type of server are as follows: The projected needs are for a total increase in capacity of $90$ Secure servers and $90$

Super Secure servers. Management wants to determine which data centers to update

to meet projected needs and, at the same time, minimize the total cost of the added

capacity.LO $2,$ LO $4,$ LO $5$ a$.$ Formulate a binary integer programming model that could be used to

determine the optimal solution to the capacity increase question facing

management.

b$.$ Solve the model formulated in part $($a$)$ to provide a recommendation for

management.