The graph below is used for problems $10$ and $11.$

$10.$ Using the Greedy Algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex B$,$ the first edge chosen when constructing the circuit is

a$)BD.$

b$)AB$

c$)CD$

d$)BC$

$11.$ After applying the Greedy Algorithm, the total weight of the circuit constructed is

a$)23$

b$)48$

c$)45$

d$)$ none of these