# find maximum value of F

F = (4*x+4*y+9*z-2*w),
G = (2*x+2*y +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

Homework ?

Use Lagrange multipliers?

Where are you stuck?

Still homework or not ?

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

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

stronglyadvisable, 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...)).