find maximum value of F

asked 2020-10-14 04:45:51 -0500

F = (4x+4y+9z-2w), G = (2x+2y +z+ w)==0, H = (x^2+y^2+z-4)==0,

  • x ,y, z, w is symbolic expressions in 4 variables.
  • The symbolic expressions G and H represent constraints.
  • find the maximum value of F , subject to the constraints G=0 and H=0 ?????????

  • please help me

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Comments

Homework ?

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2020-10-14 06:14:09 -0500 )edit

Use Lagrange multipliers?

slelievre gravatar imageslelievre ( 2020-10-14 17:17:18 -0500 )edit

Where are you stuck?

slelievre gravatar imageslelievre ( 2020-10-15 06:50:04 -0500 )edit

Still homework or not ?

Hint : the maximum you seek is $\displaystyle\frac{516}{11}$...

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2020-10-16 08:52:14 -0500 )edit

Another hint : in your specific case, Lagrange multipliers are not strictly necessary, and a high school-level method is sufficient...

Nevertheless, looking up "Lagrange multipliers" in Wikipedia and understanding it is strongly advisable, event if the rigorous proofs underlying it require a bit more analysis than high school-level... (Anyway, high school-level analysis postulates some properties of the real numbers, whose proof requires way more than high school-level algebra and topology (the latter being null IIRC...)).

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2020-10-16 09:18:28 -0500 )edit