In the above network, the number on each arc denotes the cost of transportation of one unit of flow on that arc, while the number in the purple box next to a node represents the external supply or demand at that node.

Consider the spanning tree T$=\{(1,2),(2,5),(5,3),(3,4)\}$

as highlighted by the bold arrows in the above figure. For your convenience, other non$-$tree arcs are greyed out.

Assume that node $5$ is selected as the root node. What are the values of yi

$($the cost of transportation of one unit of flow from the root node to the i

$-$th node$)$ for the remaining nodes on the tree T

$?$

Notes:

For an arc $($i$,$j$)$

of the considered spanning tree, we have yj$$yi$=$cij

$.$

In the table below, select the correct choice among the given choices in each row of the table $($except the row for the root node$).$

Select the correct choice among the given choices

Node Value of yi

$1$

y$1$

$=$

$2$

y$2$

$=$

$3$

y$3$

$=$

$4$

y$4$

$=$

$5$

y$5=0$