HW$1$: Intro to Network Models

Graham Krackers has $3$ plants where it produces $($you guessed it$)$ graham crackers that it then ships to $5$ warehouses. The table below gives the plant and warehouse locations as well as the cost to ship between each plant and warehouse.

Figure $1$: Locations of Graham Krackers plants and warehouses

$\backslash$table$[[$$$/$ton$,\backslash$table$[[$Warehouse $1],[($Newark$)]],\backslash$table$[[$Warehouse $2],[($Chicago$)]],\backslash$table$[[$Warehouse $3],[($Atlanta$)]],\backslash$table$[[$Warehouse $4],[($Dallas$)]],\backslash$table$[[$Warehouse $5],[($Los Angeles$)]],$Supply$],[$Plant $1,,6,5,12,19,180$ tons$],[($Pittsburgh$),,,,,,],[$Plant $2,10,4,8,5,14,280$ tons$],[\backslash$table$[[$Plant $3],[($Omaha$)]],13,9,3,6,10,150$ tons$],[$Demand$,120$ tons,$100$ tons,$160$ tons,$80$ tons,$150$ tons,$]]$

a$)$ Draw the network diagram for this problem.

b$)$ Formulate a concrete model that would allow Graham Krackers to satisfy demand of the warehouses at minimum cost.

c$)$ Formulate a parameterized model that would allow Graham Krackers to satisfy demand of the warehouses at minimum cost.