Question

I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20 per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $160 for the project, what are the dimensions of the garden with the largest area I can enclose? ]
__ ft(smaller value)
___ ft (larger value)
___ft^2

Answer 1

Let x = length of southern boundary
let y= length of east/west boundary. Now calculate costs which is to sum up to $160
20x+20y = $160 divide thru by 20 getting
x + y = 8
x=8 - y Now the area will be x*y
A=(8-y)(y)
A=8y-y^2 now compute A' ,
A'=8-2y for max let A'=0
0=8-2y
2y=8
y=4
x=8-y=4
Check out cost
4($20) + 8($10)= $160 Those are dimensions
32 sq ft.

Dont' know what the minimum would be that seems like a silly question. Maybe somone will compute the minimum area and spend $160.

Answer 2

Error alert. Area will be width x length or 4 X 4 = 16 sq ft.

Answer 3

Not 32 sq ft.