Question $2.(20$ points$)$: Suppose that the decision variables of a mathematical programming model are: $1$ workeriis assigned to station j during shift t xi$,$j$,$t $=0$ otherwise STOR$415$: Introduction to Optimization$-$ Spring $2024$ Student$$s name: where i $=1,...,100,$ j $=1,...,15,$ and t $=1,...,4.$ Assume that each worker is assigned to at most one station in any given shift. We say that a station is occupied if there is at least one worker. Formulate one or more linear integer constraints that model the stated condition in each part below. Introduce, and clearly define, additional decision variables if necessary. A$)$ During each shift, there must be at least $2$ workers on each station. B$)$ Onstation $6$ and $7,$ workers $22,24,$ and $33$ cannot all work together on any shift. C$)$ Thenumberof workers on station $3$ must be the same for all shifts. D$)$ During shift $2,$ either stations $8$ and $9$ have at least $3$ workers, or station $3$ has at least $3$ workers