A$-$One company has established a distribution system for the supply of critical components. Currently there are two origins for these components, which must be shipped to three plants. The current network has the following characteristics:

COSTSPlant $1$Plant $2$Plant $3$Supplysource $1$$$7$$$11$$$10400$source $2$$$3$$$6$$$5600$Demand$600450550$

The firm has identified two potential sites for a third component source; these are identified as Source A and Source B$.$ From A$,$ the costs to ship would be $$13$ to Plant $1,$ $$8$ to Plant $2,$ and $$12$ to Plant $3.$ From B$,$ these costs would be $$9,$ $$8,$ and $$7.$ The new source, wherever it is located, will have a capacity of $550$ units. Solve with the transportation method. Which site should be selected?

a$.$ Is the problem balanced? $[$ Select $]["$no$",$ "yes"$]$ If not, which area is short? $[$ Select $]["$demand; $150$ units", "demand; $75$ units", "neither, the problem is balanced", "supply; $50$ units", "supply; $100$ units"$]$

a$.$ What is the cost when evaluating Source A$?[$ Select $]["$$$9,450","$$$10,200","$$$4,500","$$$9,600","$$$9,300"]$

b$.$ What is the cost when evaluating Source B$?[$ Select $]["$$$1,200","$$$9,650","$$$8,760","$$$10,100","$$$8,850"]$

c$.$ Which site should be selected?