Quiz 7 Hint for 1

Because the values of x, y and z are non-negative, this is a little different from a standard Lagrange multiplier problem. The set of points satisfying the constraint is a plane; the set of points on the plane with non-negative coordinates forms a triangle. On the boundary of the triangle the function is zero, so the max must occur inside the triangle, since the function is positive at some of the points inside the triangle.

To find this maximum we can use the method of Lagrange multipliers. To do this, follow the procedure in Lagrange multipliers: A Review, and in the end consider only critical points with positive coordinates. The first step is to find the gradient of the function we are trying to optimize and the gradient of the constraint function. What are they in this problem?
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