2.3. LAGRANGE MULTIPLIERS 67
Problem 2.50 If
f .x; y; z/ D x
2
C 4y
2
C 9z
2
and x Cy C z D 60, find the values of x, y, and z that maximize and minimize f .
Problem 2.51 If
h.x; y; z/ D x
2
y
2
C z
2
and x Cy C z D 6, find the values of x, y, and z that maximize and minimize h.
Problem 2.52 If
q.x; y; z/ D x
2
y
2
2z
2
and x Cy C z D 300, find the values of x, y, and z that maximize and minimize q.
Problem 2.53 Find the largest point in intersection of
x C 2y C 3z D 4
and a cylinder of radius 2 centered on the z-axis.
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