word problem precalc

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A farmer wishes to enclose a pasture that is bordered on one side by a river(only 3 sides require fencing), She has decided to make a rectangular shape and will use barbed wire to make it. There are 600 ft of wire for the project, and will use all the wire .What is the maximum area that can be enclosed by the fence?(hint:use info to create a quadratic function for the area then find the maximum of the function).

Please show me step by step how to solve this! 

Jul 17th, 2015

Thank you for the opportunity to help you with your question!

sum of all three border :  2x+y = 600  hence we can write ,  y = 600-2x

Area of rectangular land, A = xy 

or we can write A = x(600-2x)  ; A = 600 x - 2x²

To find the maximum possible area, let us find its first derivative
A' = 600-4x  = 0
  solving we get ,  4x = 600  ;  or  x  = 150 ft
y = 600- 2x = 300 ft

Maximum possible  Area = 150×300 = 45000 square ft

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Jul 17th, 2015

how did you get 600-4x/ where did the 4 come from?

Jul 17th, 2015

derivative of x^2  is 2x

since d/dx (x^n) = n x^(n-1)

A = 600 x - 2x²
To find the maximum possible area, let us find its first derivative
A' = 600* d/dx(x) -2 d/dx (x² )

hence  A' = 600-4x  =0

Jul 17th, 2015

Can it be solved another way such as with factoring or quadratic formula? I have never learned the derivative method you are talking about 

Jul 17th, 2015

are you not studying calculus ???

Jul 17th, 2015

differentiation ?


Jul 17th, 2015

I am studying precalculus 

Jul 18th, 2015

We have got area A  = 600 x - 2x² 

Since A represents a quadratic equation    hence we can re-write A the exponents in descending order:

A =- 2x² +600 x 


The graph of A will be parabola and, since , the parabola will have a maximum point as its vertex. The y-coordinate of the vertex will represent our greatest area. To proceed, we need to find the value of the x-coordinate of the  vertex  (that is, the value of l in our equation).

x = -b/2a = -600/2(-2) = 150 Ft

Substituting this value and find y = 300 ft 



Jul 18th, 2015

Thankyou so much! 

Jul 18th, 2015

you are most welcome ... please remember me for your math/science problems


Jul 18th, 2015

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