$($a$)$ Formulate a binary integer programming model that could be used to determine the optimal solution to the capacity increase question facing management. If required, round your answers to one decimal place.

Let $x_i\{\begin{array}{ccc}1& if\text{d}\text{a}\text{t}\text{a}\text{c}\text{e}\text{n}\text{t}\text{e}\text{r}iis\text{u}\text{p}\text{d}\text{a}\text{t}\text{e}\text{d}& \\ 0& if\text{d}\text{a}\text{t}\text{a}\text{c}\text{e}\text{n}\text{t}\text{e}\text{r}iis\text{n}\text{o}\text{t}\text{u}\text{p}\text{d}\text{a}\text{t}\text{e}\text{d}& \end{array}$

$($b$)$ Solve the model formulated in part $($a$)$ to provide a recommendation for management. If required, round your answers to one decimal place.

Optimal solution:

Total Cost: $ Millions