Given this problem of minimum$-$cost flow problem in which the source is nodle $1$ and the sink is node $7.$ For each arc $($i$,$j$)$ let xij the decision variable that represents the quantity of flow passing through this arc.

Chose the right answer:

a$.$ The optimal value for the solution x$12=2,$ x$13=2,$ x$25=0,$ x$24=2,$ x$34=0,$ x$36=2,$ x$45=1,$ x$46=1,$ x$57=1,$ x$67=3$ is $4.$

b$.$ x$12=1,$ x$13=0,$ x$25=1,$ x$24=0,$ x$34=0,$ x$36=0,$ x$45=0,$x$46=0,$ x$57=1,$ x$67=0$ is a feasible solution

c$.$ x$12=2,$ x$13=3,$ x$25=1,$ x$24=1,$ x$34=1,$ x$36=2,$ x$45=1,$ x$46=1,$ x$57=2,$ x$67=3$ is a feasible solution

d$.$ The optimal value of x$12=1,$ x$13=2,$ x$25=1,$ x$24=0,$ x$34=0,$ x$36=2,$ x$45=0,$ x$46=0,$ x$57=1,$ x$67=2$ is $2$