$($a$)$ Notice that this problem has three special characteristics:$(1)$ number of sources $=$ number of destinations, $(2)$ each supply $=1,$ and $(3)$ each demand $=1.$ Transportation problemswith these characteristics are of a special type called the assignment problem $($as described in Sec. $9\mathrm{.}3).$ Use the integer solutions property to explain why this type of transportation problem can be interpreted as assigning sources to destinations on a one$-$to$-$one basis.$($b$)$ How many basic variables are there in every BF solution? How many of these are degenerate basic variables $(=0)?$D$,$I $($c$)$ Use the northwest corner rule to obtain an initial BF soluton.

$9\mathrm{.}2-1.$ Consider the transportation problem having the following parameter table:

$\backslash$table$[[,,$Destination,Supply$],[,,1,2,3,4],[$Source$,1,7,4,1,4,1],[2,4,6,7,2,1],[\backslash$table$[[3],[4]],8,\backslash$table$[[5],[7]],4,6,1],[$Demand$,4,6,\frac{7}{1},6,3,1],[,,1,1,1,1,$yen$]]$