how to get the largest AREA?
The fencing for the southern boundary costs $6 per foot, and the fencing for the east and west sides costs $3 per foot. If I have a budget of $240 for the project, what are the dimensions of the garden with the largest area I can enclose?
- notthejakeLv 79 years agoFavorite Answer
Area = xy, where x is the east-west length, and y is the southern boundary
does this mean you're only fencing the east, west, and south sides, and the north side is against some border that doesn't need fencing?
cost of fence: 6y + 2x(3) = 6x + 6y = 240
x + y = 40
y = 40 - x
area = xy = x(40 - x)
this is a parabola that opens downward with zeros at x = 0 and x = 40
the vertex, a maximum, will be halfway between them at x = 20
when x = 20, then y = 40 - 20 = 20
the maximum area will be 20(20) = 400
this will be with the east and west sides and southern side all having a length of 20
the fact that the southern boundary is twice as expensive makes up for the fact that you aren't fencing the northern boundary