A manufacturing organization has presently three warehouses with capacities of $30,10,$ and $50$ units, respectively. Operating the

three warehouses incurs fixed operating costs of $$25,$$$50,$ and $$45,$ respectively. The first warehouse could be expanded by up

to $20$ units for a cost of $$1$ per unit capacity. It is also possible to close any of the existing warehouses, in which case no operating

costs are incurred at that site. Furthermore, two additional sites have been identified, where new warehouses might be opened.

The costs to open the two new warehouses are $$15$ and $$25,$ and their respective capacities are $20$ and $30$ units. As far as demand

goes, there are presently three customers with demands of $20,60,$ and $40$ units. These demands must be satisfied exactly. The

unit transportation costs between the existing and potential warehouses and the customers are shown in the following table where

the first three supply points refer to the existing warehouses, while the last two supply points symbolize the potential new

warehouses. Formulate and solve an integer programming problem that minimizes the total cost.