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

$\backslash$table$[[$Plant$,$Capacity $($units$)],[$Augusta$,300],[$Tupper Lake,$100]]$

$\backslash$table$[[$Distributor$,$Capacity $($units$)],[$Boston$,150],[$New York,$100],[$Philadelphia$,150]]$

The unit transportation costs $($in $$)$ for shipments from the two plants to the two warehouses and from the two warehouses to the three distributors are as follows:

$\backslash$table$[[$Plant$,$Warehouse$],[$Albany$,$Portsmouth$],[$Augusta$,7,5],[$Tupper Lake,$3,4]]$

$\backslash$table$[[,$Distributor$],[$Warehouse$,$Boston,New York,Philadelphia$],[$Albany$,8,5,7],[$Portsmouth$,5,6,10]]$

Adirondack Paper Mills, Inc., operates paper plants In Augusta, Malne, and Tupper Lake, New York. Warehouse facilitles are located In Albany, New York, and Portsmouth, New Hampshire. Distributors are located In Boston, New York, and Philadelphla. The plant capacitles and distributor demands for the next month are as follows:

$\backslash$table$[[$Plant$,$Capacity $($units$)],[$Augusta$,300],[$Tupper Lake,$100]]$

$\backslash$table$[[$Distributor$,$Capacity $($units$)],[$Boston$,150],[$New York,$100],[$Philadelphia$,150]]$

The unit transportation costs $($in $$)$ for shipments from the two plants to the two warehouses and from the two warehouses to the three distributors are as follows:

$\backslash$table$[[$Plant$,$Warehouse$],[$Albany$,$Portsmouth$],[$Augusta$,?,5],[$Tupper Lake,$3,4]]$

$\backslash$table$[[$Warehouse$,$Distributor$],[$Boston$,$New York,Philadelphia$],[$Albany$,8,5,7],[$Portsmouth$,5,6,10]]$

a$.$ Draw the network representation of the Adirondack Paper Mills problem. $(6$ points$)$

b$.$ Formulate the Adirondack Paper Milis problem as a linear programming problem. You do not need to solve the model. $(10$ points$)$