$1.$ Formulate the game matrix for this problem. Assume zero$-$sum game and pointof view of Company X$.$

$2.$ Where should each firm locate its store? Is there a saddle point? What is thevalue of the game?

$3.$ If both companies will be given $2$ additional options to locate its new stores$($Company X now plans to have $2$ stores and Company Y still plans to have $1$ store$),$ asfollows: $(1)$ three distance units to the right of A $($point D$)$; and $(2)$ Six distance units tothe left of C $($point E$).$ Both new locations alternatives will only be used by Company Xas the location of their second store. Location D has an additional $5$ customers apart from$4$ and $2$ customers that would be taken out from Location A and B$,$ respectively.Location E also has $5$ additional customers apart from $5$ and $2$ customers that would betaken out from Location B and C$,$ respectively. Formulate the new game matrix $($point ofview of Company X$)$ for this problem. Reduce the game matrix into the smallest possiblesize using the law of dominance.