While exploring a cave, Carl comes across a collection of 5-pound rock

4 x 4-lb = $44
2 x 1-lb = $4
Total weight = 18-lb
Total value = $48

w/ a maximum of 18 lbs he carry double load of the 1st & 2nd kind, which means total cost will be 2*14 + 2*11 = 50. Answer C.
Total Load in lbs will be 2*5 + 2*4 = 18

We have 5-pound rocks worth 14 each, 4-pound rocks worth 11 each, and 1-pound rocks worth 2 each.
So, value per pound of 5 pound rock = 14/5 = 2.8
value per pound of 4 pound rock = 11/4 = 2.75
value per pound of 1 pound rock = 2/1 = 2

Now we need total of 18 pound maximum.. So, we can start making combination having rocks which has max. value per pound.

So, this can be done in following ways.
1. 3 five pound rock + 3 two pound rock: Total weight = 18 pound , Total value = 14x3 + 2x3 = 48
2. 4 four pound rock + 2 two pound rock: Total weight = 18 pound, Total value = 11x4 + 2x2 = 48

So, the maximum value, in dollars, of the rocks he can carry out of the cave. = 48 dollars.

Answer A

The dollar per pound is greatest for the 5 pound rock, then the 4 pound and lastly for the 1 pound. So we should take:
Two 5 pound rocks =2*$14= 28
Two 4 pound rocks= 2*$11= 22
Total weight: 50
IMO answer is option C

P.S: We need to find the maximum value, in dollars, of the rocks he can carry out of the cave. That is why I took 5lb and 4lb rock.

Official Explanation

The ratio of dollar per pound is greatest for the 5 pound rock, then the 4 pound, lastly the 1 pound. So we should take two 5 pound rocks and two 4 pound rocks. Total weight: 2*14 +2*11 =50