Perform the network simplex method $to$ solve the minimum cost network flow problem beginning

with the initial basis $B=\{x_{52}=3,x_{2t}=3,x_{1t}=5,x_{3t}=4\}.$ The non$-$basic variables are $x_{51}=5$ and $x_{53}=4,x_{21}$

$=0$ and $x_{23}=0.In$ every iteration, dual variable ${}_5=0.$

$2-1.(2$ points$)$ Overdraw the initial basic arcs with the solid lines $in$ the following figure. Calculate and

write the dual variables. Calculate and write the reduced costs $of$ the non$-$basic variables. $2-2.(2$ points$)Is$ the initial basis optimal? Circle $(Ye\frac{s}{N}o)IfNo,$ overdraw with solid arcs the cycle along

which the circular flow $$ flows $in$ the figure and fill $in$ the blanks $in$ the table. $2-3.(2$ points$)$ Overdraw the basic arcs with the solid lines $in$ the following figure. Calculate and write

the dual variables. Calculate and write the reduced costs $of$ the non$-$basic variables. $2-4.(2$ points$)Is$ the basis optimal? Circle $(Ye\frac{s}{N}o)IfNo,$ overdraw with solid arcs the cycle along which

the circular flow $$ flows $in$ the figure and fill $in$ the blanks $in$ the table.