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ERoseM

  • 2 years ago

The management of a large store wishes to add a fenced in rectangular storage yard of 20000 ft^2 using the building as one side of the yard. Find the minimum amount of fencing that must be used to enclose the remaining 3 sides of the yard.

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  1. robtobey
    • 2 years ago
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    |dw:1352078429334:dw|

  2. ERoseM
    • 2 years ago
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    Okay, I am confused on what formula to use

  3. robtobey
    • 2 years ago
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    Called away a short time ago. area = h*w, 20000= h*w perimeter = 2h + w Solve 20000 = h*w for w and plug the result into the RHS of the perimeter equation. Take the derivative of the resulting RHS, set the derivative expression to zero and solve for h.

  4. ERoseM
    • 2 years ago
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    Thank you!

  5. robtobey
    • 2 years ago
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    You're welcome and thank you for the medal. If you have access to the Mathematica 8 program, then this problem could have been solved using the Constrained Optimization function, Minimize: \[\text{Minimize}[\{2h+w,w h==20000,w>0,h>0\},\{w,h\}] \]\[\{400,\{w\to 200,h\to 100\}\} \] The 400 is the minimum perimeter value. No knowledge of the Calculus required with this approach.

  6. ERoseM
    • 2 years ago
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    Oh, okay, thanks I didn't know about that! Thank you !

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