1. The problem statement, all variables and given/known data Find three positive numbers x, y, and z whose sum is 100 such that (x^a)(y^b)(z^c) is a maximum. 2. Relevant equations constraint: x+y+z=100 maximize: (x^a)(y^b)(z^c) 3. The attempt at a solution First I replaced the z in the maximization problem with 100-y-z. Then I took the partial derivatives of the maximization function with respect to x and to y. Solving these, I got x=100. This implies that y=-z. But the question asks for all positive numbers. I don't know what else to do...any tips?