Homework SourseA landscape architect plans to enclose a 3000 square foot re
A landscape architect plans to enclose a 3000 square foot rectangular region in a botanical garden. She will use shrubs costing $25 per foot along three sides and fencing costing $10 per foot along the fourth side. Find the minimum total cost.
Solution
x = length
y = width
xy = 3000
cost = C(x) = 10x + 25x + 25y + 25y = 35x + 50y = 35x + 50*(3000/x) = 35x + 150000/x
To minimize C(x), we have:
C\'(x) = 35 - 150000/x2 = 0
x2 = 150000/35
x = (150000/35) = 65.465
So the minimum total cost is:
C(65.465) = 4582.58
