Review the transportation problem detailed in the table below.

$\backslash$table$[[$Costs$,$D $1,$D $2,$D $3,$Supply$],[$S $1,30,12,5,20],[$S $2,10,14,12,30],[$S $3,20,11,25,75],[$Demand$,40,60,55,]]$

a$.$ Is the transportation problem balanced $[,$ if not, where is the unbalance

b$.$ Using the intuitive lowest cost method, what the the total cost of the initial solution?

c$.$ What is the optimal solution? $ $$

d$.$ If $10$ units were required to be shipped from $S1$ to D $1,$ what would be the new overall cost?