Use excel solver and show all cell values:

$($This problem is based upon $2019$ MBA graduate Sam E$.$ consulting problem discussed last Spring. 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 to stay profitable. 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$14).$

The two main SKU groups $$ Group X and Group Y$.$ Each SKU Group uses up a certain amount of warehouse space $$ Group X uses $5$ space units per unit of product and Group Y uses $9$ space unit per unit of product.

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

The number of product units that needs to be redistributed is shown below $$ by warehouse by SKU group.

The following table depicts attributes about the remaining active warehouses $$ specifically the space available to house existing SKU Group units from the $3$ closing warehouses and a measure of inventory turnover $($INV TURN$)$ for each SKU Group at each warehouse. The higher the inventory turnover measure, the quicker the products sell $($and that is $$good$).$ Weighted averages of INV TURN will impact the model solution $($see later$).$

Create an LP model that will determine how to send the two kinds of SKU units from S$23,$ S$27$ and S$15$ to the remaining $7$ active warehouses. Cost should be minimized. Your model must be very explicit in its specifications.

Other aspects of your model:

$-$ All SKU units must be sent.

$-$ The space of arriving units at an active warehouse is constrained by the space available. Refer back to $3$rd paragraph for how much space each SKU group requires.

$-$ Also, at least $50\%$ of the space requirements at each active warehouse must be used by SKU Group arrivals. This is a de facto $$balancing$$ constraint.

$-$ To make sure products are sent to where they are more likely to be sold, the INV TURN of arriving units at each warehouse must average at least $21\mathrm{.}5$ per unit.

$-$ No more than $525$ units combined of $($X$,$Y$)$ can be sent from any one closing warehouse to any one active warehouse. This is units of SKU groups, not anything to do with warehouse space. Combined X$+$Y$.$

$-$ At the end, make sure integer units are sent.