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.
:
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/W}}}
:
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/W}}}
C = 16.5({{{5300/W}}}) + 19.5W
:
Plot this on your graphing calc: y = 16.5(5300/x) + 19.5x
{{{ graph( 300, 200, -50, 150, -1000, 5000, 16.5(5300/x)+19.5x)  }}}
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