Question
Hello can u help? I need a solution to calculus problem I have $500.00 to spend on fencing for a garden. The fence for the street side costs $30.00 per foot and the other three sides cost $10.00 per foot. what dimensions will give you a rectangle for the largest possible area?
How do you know it is for max area?
How do you know it is for max area?
Answers
Steve
with street side length x, and yard width y, then the cost is
c = 30x + 10(x+2y)
c=500, so
500 = 40x + 20y, so
y = 25 - 2x
the area is given by
a = xy = x(25-2x) = 25x - 2x^2
da/dx = 25-4x
da/dx=0 when x = 6.25. So, the yard is
6.25 x 12.5
The area has a max or min where da/dx = 0. Since a(x) is a parabola opening downward, it is a max.
c = 30x + 10(x+2y)
c=500, so
500 = 40x + 20y, so
y = 25 - 2x
the area is given by
a = xy = x(25-2x) = 25x - 2x^2
da/dx = 25-4x
da/dx=0 when x = 6.25. So, the yard is
6.25 x 12.5
The area has a max or min where da/dx = 0. Since a(x) is a parabola opening downward, it is a max.