SOLUTION: my friend has $828 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $14/foot on one side, and cheaper metal fencing which costs $9 foot o

Question 881296: my friend has $828 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $14/foot on one side, and cheaper metal fencing which costs $9 foot on the other three sides.
What are the dimensions of the garden with the largest area she can enclose.
length for cedar side
width for the other side
What is the largest area that can be enclosed?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = length of the garden in feet
Let = width of the garden in feet
Let = the area of the garden in ft2
---------------------
(1)
(1)
----------------------------
(2)
from (1):
(1)
(1)
-------------------------------
By substitution:
(2)
(2)
---------------------------------------
I can say then:
(2)
The maximum occurs at:

Plug this back into (1)
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
------------------------------
The cedar side is 18 ft
The maximum area is 414 ft2
---------------------------------
Here's the plot:

RELATED QUESTIONS
My friend has $270 to spend on a fence for her rectangular garden. She wants to use cedar (answered by ikleyn)

A garden has a width that is 25 feet less than twice the length, and a length that is 10... (answered by macston)

Susan is going to fence a rectangular flower garden in her back yard. She has 50 ft of... (answered by checkley77)

Studying quadratic equations. Can you help with an equation for this word problem?... (answered by TimothyLamb,josgarithmetic)

Pls help me with this. It's really hard!! A farmer wants to make a rectangular garden of (answered by bucky,checkley75,Fombitz)

A dog owner wants to enclose a rectangular area and has $840 to spend on fencing. She... (answered by ikleyn)

a backyard farmer wants to enclosed a rectangular space for a new garden withen her... (answered by greenestamps)

Jane has 64 feet of flexible plastic fence to enclose a garden. She wants to make either... (answered by Alan3354)

Charlize has a fence around her 15 foot by 20 foot garden. If she decides to reconfigure... (answered by ankor@dixie-net.com)