In order to solve this sentence you must make terms out of the words. Answer: 1 + (1x)
Let the length of the north and south sides be x, then the length of the east and west side is 32/x.
The total fencing needed is the perimeter of the rectangle = 2x + 2(32/x) = 2x + 64/x
Cost of fencing the north and south sides is 2(2x) = 4x
Cost of fencing the east and west sides is 4(64/x) = 256/x
Total cost (C(x)) of fencing the vegetable patch is 4x + 256/x
For minimum cost dC/dx = 0
4 - 256/x^2 = 0
4x^2 - 256 = 0
x^2 = 64
x = 8
Therefore, the <span>dimensions of the vegetable patch with the least expensive fence is
</span><span>north and south sides = 8 ft
</span><span>east and west sides = 32/8 = 4 ft</span>
Sevenhundred and eighty thousand
