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Author Question: Use Lagrange multipliers to find the point P(x1, y1, z1) on the sphere (x - 3)2 + (y +2)2 + (z - 5)2 ... (Read 77 times)

jlmhmf

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Question 1

Let  pi  > 0, i = 1, 2, 3,..., n be real numbers such that = 4.
Find the maximum value of f(x1, x2, x3,..., xn) = x11/p1x21/p2x31/p3... xn1/pn  subject to the constraint = 12,  xi ≥  0, i = 1, 2, 3,..., n.

Question 2

Use Lagrange multipliers to find the point  P(x1, y1, z1) on the sphere (x - 3)2 + (y +2)2 + (z - 5)2 = 9  and the point Q (x2, y2, z2 ) on the plane  x + 2y - 2z = 7 where the distance between P and Q is minimum and determine this minimum distance.
◦ P (2, -4, 7), Q (5, 2, 1); minimum distance 9 units
◦ P (2, -4, 7), Q (1, -6, 9); minimum distance 3 units
◦ P (4, 0, 3), Q (5, 2, 1); minimum distance 3 units
◦ P (4, 0, 3), Q (3, -2, 5); minimum distance 3 units
◦ P (2, -4, 7), Q (-1, -10, 13); minimum distance 9 units


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Marked as best answer by jlmhmf on May 27, 2021

Jbrasil

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jlmhmf

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Reply 2 on: May 27, 2021
Wow, this really help


rleezy04

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Reply 3 on: Yesterday
YES! Correct, THANKS for helping me on my review

 

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