Word problem help?

Question

A farmer has 300 feet of fencing. She wants to use this fencing to construct a rectangular corral and then divide the corral in half by constructing a fence across the width of the corral. What should the outer dimensions be to maximi the area of the corral? Provide an explanation please.

Answer 1

                   y

_____________________

|                 |                 |

|                 |                 |

|                 |                 |

|                 |                 |   x

|                 |                 |

|                 |                 |

_____________________                

 

 

Using x and y for the two dimensions gives us an equation for the area of xy = A

 

We have 300 feet of fence to work with, so 3x + 2y = 300.

 

We want to maximize the area function, but we can't graph it or take its derivative while it has three variables.

(Depending on whether this is a calculus problem or an algebra II problem)

 

Solve the linear equation for y to get y = (300 - 3x)/2

 

Plug this expression for y into the area equation to get

 

x(300 - 3x)/2 = A

 

Put this quadratic in standard form by distributing the  x and dividing by 2

 

--(3/2)x² + 150x = A

 

Now you can graph it and find the highest point on the graph (in algebra), or take the derivative and set it equal to 0 (in calculus to identify the max)

 

Let me know if you have further questions.