# Optimization Problems : Largest Recatangle in a Semicircle, Minimizing Area Given Volume and Finding the Point on a Parabola Closest to Another Point

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Find the area of the largest rectangle that can be inscribed in a semicircle of radius r.

A can in the shape of a right circular cylinder is to be made to hold 1 L of oil. Find the dimensions of the can that will minimize the cost of the metal to manufacture the can.

Find the point on the parabola y^2 = 2x that is closest to the point (1, 4).

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#### Solution Summary

Optimization Problems regarding Largest Recatangle in a Semicircle, Minimizing Area Given Volume and Finding the Point on a Parabola Closest to Another Point are solved. The solution is detailed and well presented.

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