are as follows.

$\backslash$table$[[\backslash$table$[[$Data Center$],[$Number$]],$Data Center,Cost $($$ millions$),$Secure Servers,$\backslash$table$[[$Super Secure$],[$Servers$]]],[1,$Michigan,$4\mathrm{.}0,90,60],[2,$New York $1,3\mathrm{.}5,80,40],[3,$New York $2,2\mathrm{.}0,20,30],[4,$Ohio,$3\mathrm{.}5,40,80],[5,$California,$2\mathrm{.}0,50,30]]$

at the same time, minimize the total cost of the added capacity.

$($a$)$ Formulate a binary integer programming model that could be used to determine the optimal solution to the capacity increase question facing management.

Min

Secure

Super Secure

$($b$)$ Solve the model formulated in part $($a$)$ to provide a recommendation for management. Which data center$($s$)$ do you recommend Galaxy Cloud Services update? $($Select all that apply.$)$

Michigan

New York $1$

New York $2$

$$ Ohio