Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x + 5y + 4z = 15

We want to maximize subject to the constraint .

The Lagrangian is

with critical points where the partial derivatives vanish:

We assume . Then from the first three equations, we get

which leads us to a critical point at , and hence a maximum volume of .

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.

pretty sure 750 each month!

step-by-step explanation: