Demand and Supply across Network: KDGL Company

The Keystone Dry Goods Logistics Company $($KDGL$)$ provides transportation and logistics services to a range of retail companies

For the next month, KDGL needs to ensure on$-$time transportation of powdered drink shipments for one of its clients.

KDGL$\text{'}$s client owns three warehouses located in:

$-$ Los Angeles

$-$ Chicago

$-$ New York City

It uses three regional distribution centers located in:

$-$ Denver

$-$ Austin

$-$ Washington DC

The warehouses have a total supply of $65$ tons of powdered drink that must be transported to the distribution centers next month to make room for new warehouse inventory.

Each of the distribution centers have

defined minimum quantities to be

shipped. KDGL may ship more than these

quantities to ensure that all $65$ tons of

powdered drink are removed from the

warehouses, but it cannot ship less

The transportation costs $($in $\backslash$$ per ton$)$ to

ship powdered drink between each

warehouse and each distribution center

are given:

Shipping Cost $(\backslash$$ per ton$)$

Task: KDGL$\text{'}$s management needs to determine the amounts of cargo to transport from each warehouse to each distribution center to minimize the total shipping cost while satisfying the warehouse supply and distribution center demand constraints