In \triangle B A C, \angle B A C=40^{\circ}, A B=10, and A C=6. Points D and E lie on \overline{A B} and \overline{A C}, respectively. What is the minimum possible value of B E+D E+C D ?
Answer Choices
A. 6 \sqrt{3}+3
B. \dfrac{27}{2}
C. 8 \sqrt{3}
D. 14
E. 3 \sqrt{3}+9