Solution-What is the approximate change in the maximum value

Question: (a) Solve the problem, max(min) f (x, y, z) = x² + y² + z subject to g(x, y, z) = x² + 2y² + 4z² = 1

(The graph of the constraint is the surface of an ellipsoid in 3, a closed and bounded set.)

(b) Suppose the constraint is changed to x²+ 2y² + 4z² = 1.02. What is the approximate change in the maximum value of f (x, y, z)?

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What is the approximate change in the maximum value : Solve the problem, max(min) f (x, y, z) = x2 + y2 + z subject to g(x, y, z) = x2 + 2y2 + 4z2 = 1.

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