SOLUTION: By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. (a) If the cardboard is 15 in.

Question 298862: By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made.
(a) If the cardboard is 15 in. long and 7 in. wide, find the dimensions of the box that will yield the maximum volume.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
First write the equation for the volume of the box.
If you cut squares from each corner where the side of the square is x inches, then the volume of the resulting box when the flaps are folded up can be expressed as:
which simplifies to:
To find the value of x which yields the maximum of volume (V), take the first derivative of this equation and set it equal to zero.
Set this equal to zero and solve for x;
Solve by the quadratic formula: where a = 12, b = -88, and c = 105. You can do this and you should get:
or
Discard because it would result in a negative value for the length of the bottom of the box: =, so...
inches.
The dimensions of the box are:
Length, ==inches.
Width, +=inches.
Height, =inches.
The maximum volume of the box would be:

cubic inches.

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