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URGENT HELP. WORTH IT 30 POINTS

A farmer is building a pen for some goats. She is going to build a pen divided into 4 equal sections, and she needs each section to be 500 square feet (so the total combined area is 2000 square feet) One of the long sides is against a wall and will not need fencing (see the picture below). What is the minimum amount of fencing she can use? Please use calculus to solve, Please show the supporting work?

Respuesta :

raphealnwobi

The minimum amount of fencing she can use is 126.5 ft.

Equation

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the length of the long side of pen and y represent the length of the small side of pen. Hence:

xy = 2000

x = 2000/y

The perimeter (P) is:

P = x + 2y

P = 2000/y + 2y

The minimum amount is at dP/dy = 0, hence:

dP / dy = 2 - 2000/y²

2 - 2000/y² = 0

2 = 2000/y²

y = 31.6 ft.

Also:

x(31.6) = 2000

x = 63.3

P = 63.3 + 2(31.6) = 126.5 ft.

The minimum amount of fencing she can use is 126.5 ft.

Find out more on Equation at: https://brainly.com/question/2972832

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