.

Now substitute z = 4 - x + 2y. Expand. Simplify. Spadework for you to do.

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Let and find extrema in the usual way:

Solve simultaneously:

.... (1)

.... (2)

Spadework for you.

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Get the vector QP and show that QP is parallel to the normal to the plane (which is seen from the Cartesian equation of the plane to be i - 2j + k).