b$)(20$ points, $5$ points each$)$ Now suppose that, in addition to $4$ production facilities, you have made

an agreement with $2$ other production facilities you can use to produce couches. That is$,$ now you

have $6$ production facilities you can use for production. Using similar binary decision variables

you defined in part a for facility selection decision, formulate a single linear constraint for each of

the following restrictions $($the constraints must be written in mathematical notation only$).$

i$.$ If you produce at facility $4,$ you need to use at least two other facilities.

ii$.$ You can use at most $5$ production facilities.

iii. You must use at least $2$ production facilities.

iv$.$ If both facilities $2$ and $3$ are selected, then you must also select facility $5.$