Please use R$-$Studio

Cloud Services Capacity Planning. Galaxy Cloud Services operates several data centers across the United States containing servers that store and process data on the Internet. Suppose that Galaxy Cloud Services currently has five outdated data centres: one each in Michigan, Ohio, and California and two in New York. Management is considering increasing the capacity of these data centres to keep up with increasing demand. Each data centre contains servers that are dedicated to Secure data and to Super Secure data. The cost to update each data centre and the resulting increase in server capacity for each type of server are as follows:

$\backslash$table$[[$Data center,Cost$($$millions$),$Secure Servers,Super Secure Servers$],[$Michigan$,2\mathrm{.}5,50,30],[$New York $1,3\mathrm{.}5,80,40],[$New York $2,3\mathrm{.}5,40,80],[$Ohio$,4,90,60],[$California$,2,20,30]]$

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 centres to update to meet projected needs and, at the same time, minimize the total cost of the added capacity. In particular, you have been asked to

$($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.