I would like to fence in a rectangular area in my back yard for my dog. I would

Question

I would like to fence in a rectangular area in my back yard for my dog. I would like to use chain link fencing, which is only $5 per lineal foot, for both sides and the front. The guy that lives behind me has a dog, and if the two of them see each other, they will be barking all of the time. So, I will need to use solid redwood fencing at $22 per lineal foot to do the back wall. I would like the area to be 400 square feet, but do it at a minimum cost. How much of the redwood fencing will I need to buy?

Explanation / Answer

let the length of area be x, and breadth be y. then xy = 400, and cost = (2y + x)*5 + 22x, so cost = (800/x + x)*5 + 22x = (4000/x + 27x), now we need to minimize cost, so x = 12.17feet. so redwood fencing required is 12.17feet

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