$1.$ Adirondack Paper Mills, Inc. operates paper plants in Augusta and Tupper Lake. Warehouse facilities are located in Albany and Portsmouth. Distributors are located in Boston, New York, and Philadelphia. The plant capacities and distributor demands for the next month are as follows:

Plant Capacity $($units$)$

Augusta $450$

Tupper Lake $150$

Distributor Demands $($units$)$

Boston $200$

New York $100$

Philadelphia $200$

The unit transportation costs for shipments from the two plants to the warehouses and form the warehouses to the three distributors are shown below.

Warehouse

Plant Albany Portsmouth

Augusta $75$

Tupper Lake $34$

Distributor

Warehouse Boston New York Philadelphia

Albany $857$

Portsmouth $5610$

Develop a network representation of this problem and formulate the problem as a linear program.