# volume of largest rectangular box

• Nov 1st 2009, 07:08 PM
zpwnchen
volume of largest rectangular box
Quote:

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 http://webwork.asu.edu/webwork2_file...de90fff811.png. Largest volume is
i have no idea how to get started. pls help.
• Nov 1st 2009, 08:03 PM
zpwnchen
$V = xyz = 36yz - 4y^2z -9yz^2$
$V_{y} = 36z - 8yz -9z^2 = 0$
$V_{z} = 36y - 4y^2 - 18yz =0$

then solve for y,z and i got

y=0, z=0
y=5/2, z = 16/9

and substitude y and z into V and i got V = 400/9