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

ID: 2838464 • Letter: I

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 600 Square Feet. I fenced in the back of my property last year with a nice quality fence. It cost $40 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 ($15 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

The cost of the fence is 40 L + 2*15w = 40L + 30w

LW = 600

Thus, W = 600/L

We minimize 40 L + 30 * 600/L = 40L + 18000/L

Take the derivative.

We get 40 - 18000/L^2

40 - 18000/L^2 = 0

40L^2 = 18000

L^2 = 450

L = 15 sqrt(2)