I need to fence in an area in my back yard to create a kennel for my dog. I woul

Question

I need to fence in an area in my back yard to create a kennel for my dog. I would like the area of the kennel to be 400 Square Feet. I fenced in the back of my property last year with a nice quality fence. It cost $20 per lineal feet. To create my kennel, I only need to make 3 more sides. But, I want to keep the cost at a minimum. Since I will only see the front side of the fence from my living room window, I would like the front side of the kennel to be made of the same material as the existing fence. I can get by with a cheaper fence ($5 per lineal feet) on the two sides. How much of the Nice Quality Fence will I need to buy to minimize the cost of my kennel?

Explanation / Answer

price = 20*x + 2*5*y = 20 x + 10 y

area = xy = 400 so y = 400/x

P = 20*x + 4000/x

P' = 20 - 4000/x^2 = 0

20 x^2 = 4000

x =sqrt(200) = 14.14

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