1. Assume we have function V(x,y,z) = 2x2y2z = 8xyz and we wish to maximise this function subject to the constraint x^2+Y^2+z^2=9. Find the value of V at which the max occurs 2. Function: V(x,y,z) = 2x2y2z = 8xyz Constraint: x^2+Y^2+z^2=9 3. So far I have gone Φ= 8xyz + λ(x^2+y^2+z^2 - 9) ∂Φ/∂x = 8yz + 2λx = 0 equation 1 ∂Φ/∂y = 8xz + 2λy = 0 equation 2 ∂Φ/∂z = 8xy + 2λz = 0 equation 3 x^2 + y^2 + z^2 = 9 so then I have multiplied equation 1 by x, 2 by y, and 3 by z so im left with 8xyz + 2λx^2 = 0 8xyz + 2λy^2 = 0 8xyz + 2λz^2 = 0 add these together and 24xyz +2λ(x^2 + y^2 + z^2) I know that x^2 + y^2 + z^2 =9 and v=8xyz so 3V=-18λ V=-6λ Now I have no idea how to go about the next stage, I am struggling to rearrange the equations to get an answer.