<PRE><B>Question 490575</B>
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 = {{{(120-3L)/2}}}
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 = {{{(-60)/(2*-1.5)}}}
L = {{{(-60)/(-3)}}}
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</PRE>