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cloudx · 02-28-2009

Postal regulations specify that the combined length and girth of a parcel sent by parcel post may not exceed 108 in. Find the dimensions of the rectangular package that would have the greatest possible volume under these regulations. (Hint: Let the dimensions of the box be x'' by y'' by z''. Then 2x + 2z + y = 108, and the volume V = xyz.

Show that V = f(x,z) = 108xz - 2(x^2)z - 2x(z^2). Maximize f(x,z).)

There will be three answers. The longest side, shortest side, and middle.

02-28-2009	#1
cloudx Join Date: Feb 2009 Posts: 2	Multivariable Optimization problem Postal regulations specify that the combined length and girth of a parcel sent by parcel post may not exceed 108 in. Find the dimensions of the rectangular package that would have the greatest possible volume under these regulations. (Hint: Let the dimensions of the box be x'' by y'' by z''. Then 2x + 2z + y = 108, and the volume V = xyz. Show that V = f(x,z) = 108xz - 2(x^2)z - 2x(z^2). Maximize f(x,z).) There will be three answers. The longest side, shortest side, and middle.