Quiz 7, Second Hint for 1

In this problem, f(x,y,z)=xyz. So the gradient of f is:

The constraint is the relation between the variables x, y, and z. in this problem we know that x+2y+2z=108, so that is the constraint. Note that it is also in the form g(x,y,z)=c so we can use g(x,y,z)=x+2y+2z as the constraint function. The gradient of g is:

Remember that we want to find the points that satisfy the constraint equation, at which the gradient of f is parallel to the gradient of g (Why?). This gives the following system of equations:

So far we have one vector equation and one scaler equation. Rewrite the vector equation as a system of linear equations. What do you get?

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Lagrange multipliers: A Review

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