Question

A farmer wishes to fence in a rectangular field. If north-south fencing costs $3 a yard and east-west fencing costs $2 a yard, what are the dimensions of the field of maximum area that can be fenced in for $600?

Answer 1

Let the north-south length be W and the east-west length be L.
Target function:
A = WxL, where A is the area of the fence.

Restriction:
3(2W) + 2(2L) = 600

Subsitution:
A = W(150 - 1.5W)

Differentiate A with respect to W,
A' = 150 - 1.5W - 1.5W

Solve A' = 0 for W,
W = 50 yard
L = 75 yard

Answer 2

do u get this

Answer 3

Yes, thank you :)