for three variables,

$maxf(x,y,z)=xyz\phantom{\rule{0ex}{0ex}}\text{s.t.}\text{}\text{}(\frac{x}{a}{)}^{2}+(\frac{y}{b}{)}^{2}+(\frac{z}{c}{)}^{2}=1$

where $a,b,c$ are constant

how to solve the maximization optimization problem?

thank you for helpin

$maxf(x,y,z)=xyz\phantom{\rule{0ex}{0ex}}\text{s.t.}\text{}\text{}(\frac{x}{a}{)}^{2}+(\frac{y}{b}{)}^{2}+(\frac{z}{c}{)}^{2}=1$

where $a,b,c$ are constant

how to solve the maximization optimization problem?

thank you for helpin