(a) Given a function f(x,y,z)= 3x +2y + 6z', constrained according to the relation x +...

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(a) Given a function f(x,y,z)= 3x +2y + 6z', constrained according to the relation x + y+z = B (where B is a constant), use the method of Lagrange Multipliers to find the extremum value of f (in terms of B). (13 marks) (b) Show, using the method of Lagrange Multipliers, that the extremum value of the function f (x,y,z)=xyz, subject to the constraints x+y+z = 30 and x+ y-z=0, is f =15' /4. (a) Given a function f(x,y,z)= 3x +2y + 6z', constrained according to the relation x + y+z = B (where B is a constant), use the method of Lagrange Multipliers to find the extremum value of f (in terms of B). (13 marks) (b) Show, using the method of Lagrange Multipliers, that the extremum value of the function f (x,y,z)=xyz, subject to the constraints x+y+z = 30 and x+ y-z=0, is f =15' /4.