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Calc 1 homework help!! Urgent!!!?
A rancher wants to fence in a rectangular area of 7000 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do this?
Could you please write out the two functions you used, at the least?
Thank you!!
1 Answer
- AshLv 72 years ago
Let length of fence = L
and width of fence = W
Area of the field = LW\
7000 = LW
L = 7000/W ...(1)
Total length of fencing , D = 2L + 2W + W = 2L + 3W
considering the division is parallel to width
plug in (1)
D = 2(7000/W) + 3W
D = 14000/W + 3W ....(2)
To find optimal length derive (2) with respect to W and equate to 0
D' = -14000/W² + 3
0 = -14000/W² + 3
3 = 14000/W²
W² = 14000/3
W = 68.3 ft
plug in (1)
L = 7000/(68.3) = 102.5 ft
Total length of the fencing = 2(102.5) + 3(68.3) = 409.9 ft
