WarmMart want to open some new depots to serve three super stores at $1,$ B and C$.$ The potential locations of depots are I, II$,$ III. The costs to open depots are $$17$M$,$ $$20$M$,$ $$15$M $($M denotes million$)$ respectively. The costs for serving all orders of A from $1,$ II$,$ and lIl are SSM$,$ S$4$M$,$ SOM respectively. The costs for serving all orders of B from

$1,$ Il$,$ and Ill are $$3$M$,$ S$6$M$,$ S$5$M respectively. The costs for serving all orders of C from

$1,$ Il$,$ and III are $$6$M$,$ $SM$,$ $$4$M respectively. Also, in order to balance $($risk resilience consideration$),$ no single depot can serve more than $2/3$ of all orders of any single store.

Formulate the total cost m imization problem $($mathematical formulation$)$ for WarmMart.