Question

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane x+6y+11z=66x+6y+11z=66. largest volume is

Answer 1

This is solved in the same fashion as https://brainly.com/question/9503329.
x = 22
y = 11/3
z = 2

The largest volume is 22*11/3*2 = 161 1/3 . . . . cubic units.

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When the constraint is a plane, the x, y, z values for the maximum volume are 1/3 the x-, y-, z- intercepts.