Question

For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 50 sq. ft. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence?

Answer 1

4 dollar per foot on east and west side
2 dollar per foot on north and south side

the least expensive fense would be the LEAST use of east and west fence, thus, you need to MAXIMIZE fence on north and south side...

Now think, what are two numbers that can multiply to 50?

1x50
2x25
5x10

Remember, we want the fence to cost as little as possible. So the larger number can be reasonably the north and south side while smaller side is the east and west. If you look at the 3 dimensions i provide, 1x50 is the best possible answer.

Though not ask for... since the fence has four sides, you'd find the circumference of the 1x50 dimension. The total cost:
north: 50x$2
east: 1x$4
south: 50x$2
west: 1x$4
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sum is $208