Problems on Lagrange’s Method of Undetermined Multipliers
Problems on Lagrange’s Method of Undetermined Multipliers:
1. Find the minimum value of x2 y2 z2 subject to the conditions ax by cz = p.
Hence the required minimum value of x2 y2 z2 is
Thus the required minimum value is
2. The temperature T at any point (x,y,z) in space is T = 400 xyz2 . Find the heighest temperature at the surface of the unit sphere x2 y2 z2 = 1
Taking the equality pairs, we get
The maximum temperature: