Friday

April 18, 2014

April 18, 2014

Posted by **Anonymous** on Wednesday, April 27, 2011 at 12:35pm.

- Math -
**MathMate**, Wednesday, April 27, 2011 at 12:52pmLet squares of size x" be cut from the corners.

Volume of (open) box

=V(x)

=height*length*width

=x(11-2x)(7-2x)

=4x^3-36x^2+77x

For maximum (or minimum), equate derivative to zero:

dV(x)/dx = 12x²-72x+77=0

Solve for x to get

x=3±(√93)/6

=1.39 or 4.61 (approximately)

4.61 is clearly not a feasible solution (because 2*4.61 > 7") and will be rejected.

So the cut-outs will be squares of 1.39" (approximately).

Now verify that the solution so obtained is a maximum by ensuring that d²V(x)/dx² < 0:

d²V(x)/dx² = 24x-72 = -38.6 <0 OK.

**Related Questions**

Calculus - A box with an open top is to be made from a square piece of cardboard...

maths - an open box of rectangular base is to be made from 24 cm by 45cm ...

precalculus - a rectangular piece of cardboard measuring 14 inches by 27 inches ...

calculus - an open box is to be made from a piece of metal 16 by 30 inches by ...

algebra 2 - you can make an open box from a piece of flat cardboard. First cut ...

Calculus - Squares with sides of length x are cut out of each corner of a ...

Calculus - A SHEET OF CARDBOARD 180 INCHES SQUARE IS USED to make an open box by...

Math / Factoring - Imogene wants to make an open-top box for packing baked goods...

algebra - rectangular open-topped box is made from a 9 x 16 piece of cardboard ...

Math - The length of a piece of cardboard is two inches more than its width. an ...