Problema Solution
A rectangular field is to be enclosed on four sides with a fence. Fencing costs $2 per foot for two opposite sides, and $7 per foot for the other two sides. Find the dimensions of the field of area 870ft^2 that would be the cheapest to enclose.
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Answer provided by our tutors
Let
x = the length of the two opposite sides with fencing cost $2 per feet, x>0
y = the length of the two opposite sides with fencing cost $7 per feet, y>o
The area of the field is 870 ft^2:
xy = 870
y = 870/x
The total cost of the fence is:
C = 2*2x + 2*7y
C = 4x + 14*870/x
we need to find the minimum of the function:
C(x) = 4x + 14*870/x
click here to see the graph of the function y = 4x + 14*870/x
the minimum of function happens when x = 55.18 ft
y = 870/55.18
y = 15.77 ft
The dimensions of the field are: 55.18 ft and 15.77 ft.