Web Works #8 Spring 2009

Web Works #8 Spring 2009 - f x y x 11 y 4 xy 3 x 2 8 y 2...

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Hector Hernandez Assignment 8 MATH262, Winter 2009 due 4/17/09 at 11:59 PM. 1. (1 pt) Find the maximum value M of the function f x y x 9 y 6 5 x y 5 on the region x 0 y 0 x y 5 M 2. (1 pt) Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the mate- rial per square unit for (i) the top and bottom is 8, (ii) the front and back is 3 and (iii) the other two sides is 9. Vertical edge length = Horizontal front and back edge length = Horizontal side edge length = 3. (1 pt) Find the maximum volume of a rectangular box that can be inscribed in the ellipsoid x 2 25 y 2 25 z 2 81 1 with sides parallel to the coordinate axes. Volume = 4. (1 pt) Find the maximum and minimum values of the func- tion f x y 2 x 2 28 xy 2 y 2 2 on the disk x 2 y 2 25 Maximum = Minimum = 5. (1 pt) Find the maximum and minimum distance from the origin to a point on the curve 9 x 2 2 xy 9 y 2 8 in the x y plane. Maximum distance = Minimum distance = 6. (1 pt) Consider the function
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Unformatted text preview: f x y x 11 y 4 xy 3 x 2 8 y 2 de±ned in the unit square 0 x 1, 0 y 1. Find the maximum and minimum values of f and where they occur. The maximum value is and it occurs for x and y . The minimum value is and it occurs for x and y . 7. (1 pt) Consider the function f x y 4 x 3 11 xy 5 y 2 . Find the maximum and minimum values of f in the region de-±ned by the inequalities 1 x 1, 0 y 1 and where they occur. The maximum value is and it occurs for x and y . The minimum value is and it occurs for x and y . 8. (1 pt) Find the coordinates of the point x y z on the plane z 4 x 2 y 3 which is closest to the origin. x y z 9. (1 pt) Find the maximum and minimum values of f x y 7 x y on the ellipse x 2 4 y 2 1 maximum value: minimum value: Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR 1...
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