The Donna Mosier Clothing Group owns factories in three towns $($W$,$ Y$,$ and Z$),$ which distribute to three retail dress shops in three other cities $($A$,$ B$,$ and C$).$ The following table summarizes factory availabilities, projected store demands, and unit shipping costs:

From$\backslash$To Dress Shop A Dress Shop B Dress Shop C Factory Availability

Factory W $43335$

Factory Y $67650$

Factory Z $82550$

Store Demand $306540$

a$.$ Is the problem balanced?

$[$ Select $]$

b$.$ Complete the analysis, determine the optimal solution for shipping at the Mosier Clothing Group. $

$[$ Select $]$