# Optimization: Finding the minimum amount of fencing using implicit differentiation.

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The management of a large store wishes to add a fenced-in storage yard of 20,000 square feet, 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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#### Solution Preview

We can assume the length of the two equal sides is x, and the remaining side is y.

Then the total length of the three sides are: C=2x+y

and its area is S=x*y=20000

our question is now: Min C=2x+y with constraint: ...

#### Solution Summary

Implicit differentiation is used to solve an optimization problem.

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