US Capitals Set Covering Problem

$$ Locate $$offices$$ in State capitals $($subset of $16$ states$).$

$$ A state can either have an office $...$ or not have an office.

$$ Each state is covered by at least $1$ office.

$$ Each state is covered by no more than $2$ offices.

$$ Offices cannot be in capital that start with the same letter

$$ E$.$g$.,$ Lincoln and Little Rock NE $+$ AR

$$ Political X factor $$ offices must be located in states such that the overall

average political X factor remains less than or equal to $3\mathrm{.}75.$

$$ Coverage definition:

$$ A state is $$covered$$ if its state capital is selected.

$$ A state is $$covered$$ if a state that borderObjectives

$$ Baseline solution: Maximize population of the selected state capitals.

$$ Comparative multi$-$objective solution: First, minimize the number of

offices. Then, keeping that number $$fixed$,$ maximize the population

of the selected state capitals.

$$ Compare and contrast the solutions to these two scenarios.s that state has its state capital selected.

$$ Ex: OK covers $7$ states.