#$2$

Consider a distribution system that consists of three regional distributors, two local warehouses, and three retail stores. The augmented table below provides the shipping costs per unit of a certain product from each distributor to each warehouse and from each warehouse to each store.

$\backslash$table$[[,$Warehouse $1,$Warehouse $2,],[$Distributor $1,$$$0\mathrm{.}78,$$$0\mathrm{.}91,],[$Distributor $2,$$$0\mathrm{.}82,$$$0\mathrm{.}79,],[$Distributor $3,$$$0\mathrm{.}84,$$$0\mathrm{.}78,],[$$$0\mathrm{.}57,$$$0\mathrm{.}49,$Store $1],[$$$0\mathrm{.}44,$$$0\mathrm{.}61,$Store $2],[$$$0\mathrm{.}72,$$$0\mathrm{.}68,$Store $3],[$$$0\mathrm{.}67,$$$0\mathrm{.}61,$Store $4],[$Warehouse $1,$Warehouse $2,]]$

There are $44$ units of the product at Distributor $1,52$ units at Distributor $2,$ and $37$ units at Distributor $3.$ The demands for this period are $30$ units for Store $1,41$ units for Store $2,29$ units for Store $3,$ and $26$ units for Store $4.$

Formulate a transshipment model to minimize the total cost over the shipping network. You do not need to include the network diagram or solve the $LP.$