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As a property owner, you want to fence a garden which is adjacent to a road. The fencing next to the road must be stronger and cost $6 per foot. The fencing on the other sides cost $4 per foot. The area of garden is 2400 square feet.

Required:
Find a function that models the cost of fencing the garden.

Respuesta :

Answer:

[tex]C(x)=\dfrac{10x^2+19200}{x}[/tex]

Step-by-step explanation:

Let the dimension of the garden be x and y

Area of the graden =xy

Since the area of garden is 2400 square feet.

xy=2400

Making y the subject, we have:

[tex]y=\dfrac{2400}{x}[/tex]

Let the side next to the road =x

  • Cost of fencing Next to the road =$6
  • Cost of the other three sides = $4

Therefore, total cost of fencing the garden,

C(x,y)=6x+4x+4y+4y

C(x,y)=10x+8y

Substituting [tex]y=\dfrac{2400}{x}[/tex] derived earlier, we have:

[tex]C(x)=10x+8(\frac{2400}{x})\\C(x)=\dfrac{10x^2+19200}{x}[/tex]

Therefore, a function that models the cost of fencing the garden is:

[tex]C(x)=\dfrac{10x^2+19200}{x}[/tex]

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