Question

Chocolate Box Company is going to make open-topped boxes out of 5 × 17-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way? (Round your answer to the nearest tenth.)


Thank You for the help, I really appreciate it!

Answer 1

L = 17 - 2 h
W = 5 - 2 h

V = L W h
V = (17-2h)(5-2h)h = (17-h)(5h-2h^2)

dV/dh = (17-h)(5 - 4h) +(5h-2h^2)(-1)

= 85 - 73 h +4 h^2 -5h + 2 h^2

= 85 - 78 h + 6 h^2
where is that derivative zero?
h = [ 78 +/- sqrt (6084-2040) ]/12

h = [ 78 +/- 63.6 ] / 12

h = 11.7 impossible, plank not wide enough
or
h = 1.2 inches

Answer 2

Damon, thank you! But i tried entering it in but it said it was wrong.

Also it wants the answer in inches cubed (in^3)

Answer 3

Hey, use that h, calculate L and w
find L W h

Answer 4

Ahhh okay my bad. Thank you!!!

Answer 5

I noticed an error in Damon's solution

4th line : V = (17-2h)(5-2h)h = (17-h)(5h-2h^2)
should be : V = (17-2h)(5-2h)h = <b>(17-2h)</b>(5h-2h^2)

I had h = 1.1445