SOLUTION: Please answer this optimization problem again hehehe
1:An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corne
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Question 1135447: Please answer this optimization problem again hehehe
1:An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides.
How long should the sides of the squares be to obtain a box with the largest volume?
:
let x = the length of the side of the squares
then
(16-2x) = the width of the box
(30-2x) = the length
and
x = height of the box
:
Volume the height * width * length
V(x) = x(16-2x)(30-2x)
FOIL
V(x) = x(480 - 32x - 60x + 4x^2,)
V(x) = 4x^3 - 92x^2 + 480x
:
graphing this equation
:
x = 3.333 cm, to give a max volume of 726 cu/cm (green line)
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