$($This problem is based upon $2019$ MBA graduate Sam E$.$ consulting problem discussed Spring $2023.$ All names and contexts have been changed to protect those covered under US Code Title $27$ legislation.$)$

Due to the plethora of companies involved in the medical cannabis area, Edison's Edibles needs to consolidate its warehouses. Warehouses S$23,$ S$27$ and S$15$ are to be closed, and their $2$ main SKU groups of products redistributed to the other $7$ active warehouses $($S$2,$ S$4,$ S$6,$ S$8,$ S$10,$ S$12,$ S$14).$ After they are consolidated, they are to be sent to $4$ storefront locations $(F1,F2,F3,F4.$

The two main SKU groups $-$ Group X and Group Y$.$ You must account for them in the model separately, and warehouse space used is calculated as $x+Y.$

Our goal is to find the least cost way $($cumulative$)$ of sending Group X$,$ Y inventory from the three closing warehouses to the remaining $7,$ then from the $7$ active warehouses to the $4$ storefronts. Cost is defined below per unit of product $($all products cost the same$)$ between the corresponding warehouses and then the warehouses and the storefronts.