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Given f(x,y,z)=3x-y-3z and constraints x^(2)+2z^(2)=361, and x+y-z=4Let g=x^(2)+2z^(2)-361 and h=x+y-z-4f_(x)=lambdag_(x)+muh_(x)=>3=lambda(2x)+mu(1)f_(y)=lambdag_(y)+muh_(y)=>-1=lambda(0)+mu(1) f_(z)=lambdag_(z)+muh_(z)=>-3=lambda(4z)+mu(-1)From (2)mu=-1From (1)3=lambda(2x)-1=>lambda(2x)=4=>x=(2)/(lambda)From (3)-3=lambda(4z)+(-1)(-1)-3=lambda(4z)+1=>lambda(4z)=-4=>z=-(1)/(lambda)x^(2)+2z^(2)=361((2)/(lambda))^(2)+2(-(1)/(lambda))^(2)=361lambda=+-(sqrt6)/(19)x=(2)/(+-(sqrt6)/(19))=+-(38)/(sqrt6)z=-(1 ... See the full answer