Solve the linear program formulated in part $($a$).$ How much of each product should be produced, and what is the projected total profit contribution $($in dollars$)?$

$($P$1,$ P$2,$ P$3)=$

$60,80,60$

with profit $ $.$

$($a$)$

Formulate an integer linear program that can be used to determine the minimum number of service facilities needed and their location. $($Let

xi

be the $0-1$ variable, which is $1$ if a service facility is constructed in city i$,$ and $0$ otherwise.$)$