$[$A shameless rip$-$off of problem $5-41$ from the textbook. Please note that answers to odd numbered problems are in the back of the book$]$

The Sprague's Grocery Store chain has bought out a competing grocer store chain. However, it now has too many stores in close proximity to each other in certain cities. In Watervliet, MI the chain now has $9$ stores and it does not want any stores closer than $2$ miles to each other. Following are the monthly revenues $($in $$1000\text{'}$s$)$ from each store and a map showing the general proximity of the stores. Stores within $2$ miles of each other are circled.

$\backslash$table$[[$Store$,$Monthly Revenue$],[1,127],[2,98],[3,67],[4,92],[5,79],[6,104],[7,99],[8,74],[9,87]]$

So$,$ for instance, stores $4,7,8,$ and $9$ are all within $2$ miles of each other. Stores $5,6,7,$ and $8$ are also all within $2$ miles of each other, etc.

Sprague's wants to know which stores to keep open and which to close in order to maximize monthly revenues while adhering to the $"$no stores within $2$ miles of any other" rule.

$1.)$ What is the constraint involving store number nine?

A$)$ x$4+$ x$7+$x$8+$x

B$)$ x$9=1$

C$)$ x$4+$x$7+$x$8+$x$9>=1$

$2.)$Which of the following constraints does not apply to store number eight?

A$)$ x$4+$x$7+$x$8+$x

B$)$ x$5+$x$6+$x$7+$x

C$)$ x$2+$x$4+$x$6+$x$8+$x