problem solving

Question

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth (distance around) of no more than 114 inches. If a rectangular package has a square end, find the maximum volume of this package

Answer 1

Length (l) + girth (g) = 114 or g = 114 - l

 

Volume = l x g = l(114- l) = 114l - l²  which graphs as a parabola pointed down.  If we find its vertex, we can find its max volume

 

The l coordinate of the vertex can be found by -b/2a = -114/-2 = 57  plug this in for l in the volume equation to find the max volume:

 

114(57) - 57² = 3249 sq in