Posted by admin | Posted in Yard, Garden & Outdoor Living | Posted on 25-03-2009
Tags: architecture, design, diy, home, shed, shed construction calculator, shed construction costs, shed construction diy, shed construction plans, shed construction tips
shed construction
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Greenhouses & Garden Sheds US$ 13.45 A hands-on guide to greenhouse design and construction for homeowners and avid gardeners provides step-by-step photographs and instructions for a variety of building projects involving and relating to greenhouses and potting sheds. Original. |
Please, can I have the answer by Monday, Jan. 21?
A builder intends to construct a storage shed having a volume of 800 cubic feet, a flat roof and a square base. The cost per square foot of material is $4 for the floor and roof, $5 for the sides. What are the dimensions of the shed that minimizes the construction costs?
Hi,
To minimize costs, the shed would need to have a floor that is 10' by 10' and the height would be 8'.
If the length of the side of the square floor is "x", then the area of the floor is x². Since the roof is the same, its area is also x² for a total of 2x² square feet. They cost $4/sq ft so the cost for the floor and roof is 4(2x²) or 8x².
With each side of the floor having a length of "x", the perimeter of the base is 4x. Since the volume of the shed is to be 800 ft², then the height of the shed equals the volume divided by the area of the floor, 800/x². So, the surface area of the 4 walls is 4x(800/x²) and at $5/sq ft, the cost of the walls is 5(4x)(800/x²) = 16,000/x.
If the total cost is 8x² + 16,000/x, then let Y1 = 8x² + 16,000/x. Graph this and find the minimum. It occurs when x = 10 so the edge of the floor is 10 ft.. The height is then 8 ft. Minimum cost is $2,400.
You can also find this by taking the first derivative of f(x) = 8x² + 16,000/x to get f'(x) = 16x - 16,000/x². If you set this equal to zero and solve, you get:
16x - 16,000/x² = 0
16x = 16,000/x²
16x³ = 16,000
x³ = 1,000
x = 10 for the edge of the floor.
I hope that helps!! 
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shed construction
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shed construction
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shed construction
Keith & Aaron Building Shed - first wall -- 11-25-08.mpg
