Question

For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 50 sq. ft. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence?

Answer 1

Let x = length of north or south side.
50/x = length of east or west side.
2x($2) = cost of north or south side.
2(50/x)($4) = cost of east/west side.
total cost =4x + 400/x
Cost = C
C=4x+400/x Take the derivative
C'=4-400/x^2 For minima set to = 0
4-400/x^2 = 0 Multiply thru by X^2
4x^2 - 400 = 0 Divide thru by 4
x^2-100=0 Factor (difference of two perfect squares)
(x+10)(x-10) = 0
x=10 disregarding negative value.
North and South side is 10 ft ea.
50/x=50/10=5
East/West side is 5 ft. each.

Answer 2

Thank you so much I really appreciate it. Thank you brother.

Answer 3

ur welcome, good luck.