A fence is to be built to enclose a rectangular area of 270 square

A fence is to be built to enclose a rectangular area of 270 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 16 dollars per foot. Find the length L and width W of the enclosure that is most economical to construct.

A rectangular storage container with an open top is to have a volume of 80 cubic meters. The length of its base is twice the width. Material for the base costs 80 dollars per square meter. Material for the sides costs 6 dollars per square meter. Find the cost of materials for the cheapest such container.
Minimum cost =

Find the minimum distance from the parabola
x-y^2=0
to the point {(0,3)}.
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=8-x^2 . What are the dimensions of such a rectangle with the greatest possible area?

 

 

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