Unformatted text preview: cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area. (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) A window is to be built in the shape of a rectangle surmounted by an isosceles triangle. The area of the window must be 6m 2 . Use Lagrange Multipliers to ﬁnd the width and height of the rectangle for which the perimeter of the window will be as small as possible. (Clariﬁcations: (1) A rectangle surmounted by a triangle has the shape of a stick drawing of a house as might be drawn by a child, a rectangle with a triangle on top. (2) The window’s perimeter is made up of three sides of the rectangle and the two equal length sides of the triangle. Draw a diagram! (3) This may require some industrial strength algebra!) 1...
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 Winter '11
 JerryMetzger
 Calculus, Multivariable Calculus, lagrange multipliers

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