Find the minimum cost solution for the transportation problem detailed in the table below.

Costs D $1$ D $2$ D $3$ Supply

S $13012520$

S $210141230$

S $320112575$

Demand $406055$

a$.$ Is the transportation problem balanced

No

$,$ if not, where is the unbalance

Demand

$.$

b$.$ What is the optimal solution? $

$1,370$

c$.$ What if $17$ units needed to be sent to S$2-$ D$2.$ What is the cost?

$[$ Select $]$

d$.$ Based on letter c$.,$ what if supply at S$3$ increased by $75$ units. what is the total cost?

$[$ Select $]$