SOLUTION: A rectangular garden bounded on one side by a river is to be fenced on the other three sides. Fencing material for the side parallel to the river costs $30 per foot, and material
Algebra.Com
Question 490575: A rectangular garden bounded on one side by a river is to be fenced on the other three sides. Fencing material for the side parallel to the river costs $30 per foot, and material for the other two sides costs $10 per foot. What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular garden bounded on one side by a river is to be fenced on the other three sides.
Fencing material for the side parallel to the river costs $30 per foot, and material for the other two sides costs $10 per foot.
What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?
:
the total cost for three fenced sides
30L + 10(2W) = 1200
30L + 20W = 1200
simplify divide by 10
3L + 2W = 120
2W = 120 - 3L
W =
W = (60-1.5L)
:
A = L * W
replace W
A = L(60-1.5L)
A = -1.5L^2 + 60L
to find max area, find the axis of symmetry; x = -b/(2a)
L =
L =
L = + 20 ft is the length
Find the width
W = 60 - 1.5(20)
W = 30 ft the width
then
max area for $1200, 20 by 30 ft
:
:
Check this finding the cost for the perimeter with these dimensions
30(20) + 10*2(30) =
600 + 600 = 1200
RELATED QUESTIONS
A rectangular piece of land, bounded on one side by a river, is to be fenced on the other (answered by rfer)
A rectangular piece of land, bounded on one side by a river, is to be fenced on the other (answered by josgarithmetic)
A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house... (answered by nerdybill)
A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house... (answered by nerdybill)
A pasture is bounded by a river on one side. The farmer has 600 yards for enclosing a... (answered by ewatrrr)
A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth... (answered by ankor@dixie-net.com)
How do I solve this and how do I come up with a $$ amount?
Minimum Cost A rectangular... (answered by ankor@dixie-net.com)
CAN ANYONE HELP ME?? Minimum Cost A rectangular area adjacent to a river is to be fenced... (answered by josmiceli)
One side of the rectangular field is bounded by a river. A farmer has 100m of fencing and (answered by LinnW)