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 .

answer: do you still need this?

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .