- #1
ObviousManiac
- 37
- 0
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.
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.
V = lwh
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.
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.
