Question

A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two
opposite sides, and $2 per foot for the other sides. Find the dimensions of the field of area 900 ft2
that would be the cheapest to enclose.

Answer 1

C = 2x + 2y
C = 16x + 4y
A = xy
900 = xy
y = 900/x

C = 16x + 4(900/x)
C = 16x + 3600/x
C' = 16 - 3600/x^2
0 = 16 - 3600/x^2
16 = 3600/x^2
16x^2 = 3600
x^2 = 225
x = 25
y = 900/15
y = 60

Answer 2

square root of 225 is 15