A candy box from a piece of cardboard that measure 27 by 15inches. Squares of equal sizes will be cut out of each corner . The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume??????Thanks:D

Question

anonymous · Answer

Draw the picture first.  Then, find the equation of the volume as a function of x (the side of the corner square cutouts).  Is this a calculus problem?

anonymous · Answer

It must be.... Differentiate the volume function, and find the zeros of the derivative.  You can check to see which one is the maximum pretty easily, or use the second derivative test to see which will be the maximum.

anonymous · Answer

I think it works out something like$$V(x)=x(27-2x)(15-2x)=4x^3-74x^2+405x$$

anonymous · Answer

Then the derivative is$$V'(x)=12x^2-148x+405$$Find the zeros, then test them to determine which is the maximum.  Keep in mind that 0 < x < 15/2.

anonymous · Answer

The domain restriction is due to the physical limitations of the problem; you can't cut more than half of the fifteen inch width.