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  3. the plane x+y+z= 24 intersects the cone x2+y2= z2

The plane x+y+z= 24 intersects the cone x2+y2= z2 in an ellipse. The goal of this exercise...

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Basic Math

The plane x+y+z= 24 intersects the conex2+y2= z2 in an ellipse. The goalof this exercise is to find the two points on this ellipse that areclosest to and furthest away from the xy-plane. Thus, we want tooptimize F(x,y,z)= z, subject to the two constraints G(x,y,z)=x+y+z= 24 and H(x,y,z)= x2+y2-z2=0.

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