Farmer Brown Wants to Fence in a Rectangular Plot in a Large

Farmer Brown wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3/yard, but she needs to use special fencing which will cost $5 / yard on the south side of the plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing. Dimensions below are listed east by south.

A) $10 \sqrt { 5 }$ by $12 \sqrt { 5 }$ yards
B) $12 \sqrt { 5 }$ by $10 \sqrt { 5 }$ yards
C) 10 by 60 yards
D) 60 by 10 yards
E) $8 \sqrt { 5 }$ by $15 \sqrt { 5 }$ yards
F) $15 \sqrt { 5 }$ by $8 \sqrt { 5 }$ yards
G) 15 by 40 yards
H) 40 by 15 yards