Use Lagrange multipliers to find three numbers whose sum is 30 and the product P = x3y4z is a maximum. Choose the answer for the smallest of the three values. Question 20 options: a) 21/4 b) 5 c) 15/4 d) 3

We want to maximize subject to the constraint .

The Lagrangian is

with critical points where the derivatives vanish:

We have

Let's work with and , for which we have

The smallest of these is C. 15/4.

answer: 0

step-by-step explanation: the positive, like 5, + its opposite, like -5 would be 0

5+(-5)=0, or 5-5=0