AMC 12 2018a Problem 2

While exploring a cave, Carl comes across a collection of $5$-pound rocks worth $\$14$ each, $4$-pound rocks worth $\$11$ each, and $1$-pound rocks worth $\$2$ each. There are at least $20$ of each size. He can carry at most $18$ pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?

$\textbf{(A) } 48 \textbf{(B) } 49 \textbf{(C) } 50 \textbf{(D) } 51 \textbf{(E) } 52$