Explanation:
Area of rectangular field, A = 830 ft²
Length = l
Width = w
So we have
l x w = 830
[tex]l=\frac{830}{w}[/tex]
Fencing costs $2 per foot for two opposite sides, and $3 per foot for the other two sides.
Cost for fencing, C = 2 x 2 x w + 3 x 2 x l = 4 w + 6 l
[tex]C=4w+6\times \frac{830}{w}[/tex]
For minimum cost we have derivative is zero
[tex]dC=4\times dw-6\times \frac{830}{w^2}\times dw\\\\0=4\times dw-6\times \frac{830}{w^2}\times dw\\\\w^2=1245\\\\w=32.45ft\\\\lw=830\\\\l\times 32.45=830\\\\l=23.52ft[/tex]
Dimension for cheap enclose = 32.45 ft x 23.52 ft
