'Simple' Optimization Problem

  • #1
Just reviewing for a chapter test... I've always found optimization problems easy, but I don't have answers for these review questions so I thought I'd check my work on here.

Homework Statement


A piece of cardboard is 14 inches by 10 inches and you are going to cut out the corners and fold up the sides to form an open box. Determine the height of the box that will give a maximum volume.


Homework Equations



V = lwh


The Attempt at a Solution



Using
(10-2x) as l
(14-2x) as w
and x as the height:

V = (10-2x)(14-2x)x = 4x^3 - 48^2 +140x

dv/dx = 12x^2 - 96x + 140

0 = 12x^2 - 96x +140

x = 6.08, 1.92 or 1/3(12±√39)

.... this is where I get lost. I feel like I messed it up somewhere because I get weird numbers for x. Technically, the 6.08 number is impossible, so x would have to equal 1.92. But still, I feel uncomfortable with these numbers.
 

Answers and Replies

  • #2
jamesrc
Science Advisor
Gold Member
476
1
What makes you uncomfortable about the answer you got?

Would it make you more comfortable to compare the volume if the height were slightly above or below the height you calculated to the volume you got?
 
  • #3
Would it make you more comfortable to compare the volume if the height were slightly above or below the height you calculated to the volume you got?

haha, yes, actually. It helped quite a bit. I think I'm just too tired from too many late nights of studying... thanks for the help.
 

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