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**Queston From Mathematical Programming:?**

Find the minimum value of P(x,y,z)=Z+1/2(x^2+ y^2+1/10 z^2)

constrained by and where r is a positive constant.

Solve the problem when r=1, r=5.

Can you find the solution for general r?

(Note this is a mixed Kuhn-Tucker/ Lagrange problem. The inequality constraints are not trivial and must be taken into account.)