2018 AMC 12A 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?

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