SOLUTION: An engineer wants to build a rectangular foundation that is divided into 5 sections as shown in the figure below. If she uses 5000 linear feet of material for the division, what is

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Question 1055871: An engineer wants to build a rectangular foundation that is divided into 5 sections as shown in the figure below. If she uses 5000 linear feet of material for the division, what is the maximum area enclosed by the foundation? Round your result to the nearest square foot. Width = x Length = (5000-6x)/2
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An engineer wants to build a rectangular foundation that is divided into 5 sections as shown in the figure below.
If she uses 5000 linear feet of material for the division, what is the maximum area enclosed by the foundation?
Round your result to the nearest square foot. Width = x Length = (5000-6x)/2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Since width W = x and Length L = %285000-6x%29%2F2 = 2500-3x, the area is the product W*L

A = W*L = x%2A%282500-3x%29 = -3x%5E2+%2B+2500x.

This quadratic function has a maximum at  

x = -b%2F2a = -%282500%29%2F%282%2A%28-3%29%29 = 2500%2F6.

And this maximum value is -3%2A%282500%2F6%29%5E2+%2B+2500%2A%282500%2F6%29 = %282500%2F6%29%2A%28-3%2A%282500%2F6%29+%2B+2500%29 = %282500%2F6%29%2A%282500%2F2%29 = %282500%5E2%29%2F12 = 52.083*10^4 square feet.

On finding the maximum/minimum of quadratic functions see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.

On similar problems solved see the lessons
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Finding minimum/maximum of quadratic functions".