Question

The sum of the girth (perimeter of a cross section) and the length of a package carried by a delivery service may not exceed 108 inches. Find the dimensions of the rectangular package of largest volum

Answer 1

The sum of the girth (perimeter of a cross section) and the length of a package carried by a delivery service may not exceed 108 inches. Find the dimensions of the rectangular package of largest volume that can be sent.

Answer 2

So V=xyz. Girth= 2x+2y, which leaves z =108-2x-2y 
so 
V=xy(108-2x-2y) 
V=108xy-2x^2y-2xy^2 
Vx= 108y-4xy-2y^2 Vy=108x-2x^2-4xy 

0=y(108-4x-2y) O=x(108-2x-4y) 
y and x =/= 0 . 108= 4x+2y 108=4x+2y 
108= (2x+4y)(-2) -216=-4x-8y 
-108= -6y 
y= 18 
x=(108-4(18))/2 = 18 
z= 108-36-36 = 36 
Vxx=-4y Vyy=-4x Vxy=108-4x-4y 
D(18,18) = -4(18)(-4)(18) - (108-4(18)-4(18))^2 
=5184-1296 
=3888>0 fxx(18,18)<0 
so it goes => way