SOLUTION: A homeowner wants to enclose a 5,300 square foot rectangular garden by a fence in his backyard. If 3 sides of the fence cost $8.25 per foot and the 4th side costs $11.25 per foot,

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Question 676225: A homeowner wants to enclose a 5,300 square foot rectangular garden by a fence in his backyard. If 3 sides of the fence cost $8.25 per foot and the 4th side costs $11.25 per foot, find the dimensions that will minimize the cost of building the fence and the minimum cost of its construction.
Please help, I am very confused!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A homeowner wants to enclose a 5,300 square foot rectangular garden by a fence in his backyard.
If 3 sides of the fence cost $8.25 per foot and the 4th side costs $11.25 per
foot, find the dimensions that will minimize the cost of building the fence
and the minimum cost of its construction.
:
Let L = the length of the garden
Let W = the width
:
The required area will establish the relationship between the length and width
L*W = 5300
L = 5300%2FW
:
The cost is the sum of all the sides, one width cost more than the other
C = 8.25(2L) + 8.25W + 11.25W
C = 16.50L + 19.50W
Replace L with 5300%2FW
C = 16.5(5300%2FW) + 19.5W
:
Plot this on your graphing calc: y = 16.5(5300/x) + 19.5x
+graph%28+300%2C+200%2C+-50%2C+150%2C+-1000%2C+5000%2C+16.5%285300%2Fx%29%2B19.5x%29++
This shows a minimum when x ~ 67
:
Find the dimensions
W ~ 67 ft
L = 5300/67
L ~ 79 ft
:
Dimensions for minimum cost: 79 by 67 ft