Consider the following instance of the Transportation problem:

$\backslash$table$[[,1,2,3,$Supply$],[$A$,7,2,5,12],[$B$,3,8,1,18],[$C$,4,9,2,5],[,,,,],[$Demand$,10,10,15,]]$

a$)$ Give the total cost associated with the followhg $($basic$)$ feasible shipping solution.

$\backslash$table$[[,1,2,3,$Supply$],[$A$,10,,2,12],[$B$,,10,8,18],[$C$,,,5,5],[$Demand$,10,,,]]$

b$)$ Find the "network cost" of $($A$,2),$ i$.$e$.,$ the cost to ship from location A to location $2$ using the links in the shipping solution. Is this cost larger or smaller than the cost of shipping directly from $A$ to $2?$

c$)$ Perform a single "pivot" to find a new $($basic$)$ shipping solution that uses link $($A$,2).$