Pictured are the contours (z=0 to z=4.5 contour interval 0.5) of f(x, y) = x² + 2xy + y² together with the constraint curve ve x² + y² = 1. Explain how the graph can be used to determine the absolute extrema of the function subject to the constraint. Verify by identifying the system and including a table of values for the critical points that result from using the Method of Lagrange Multipliers.

Q: Find the maximum value of z = xy2 subject to 2x2 + y2 = 294; x ≥ 0, y ≥ 0. z =

A: Given information : z = xy2  subject to  2x2 + y2 = 294;  x≥0;  y≥0.

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Q: Find the maximum value of z = xy² subject to 2x2 + y² = 864; x ≥ 0, y ≥ 0.

A: z=xy22x2+y2=864y2=864-2x2x≥0y≥0

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