## 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.

1. robtobey

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2. ERoseM

Okay, I am confused on what formula to use

3. robtobey

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

Thank you!

5. robtobey

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

Oh, okay, thanks I didn't know about that! Thank you !