Posted by Sejul on Monday, October 10, 2011 at 2:35pm.
volume= l*w*h
2h+w=35 or w=35-2h
2h+l=35 or l= 35-2h
volume= (35-2h)(35-2h)h
dV/dh= 2(35-2h)(-2)h+ (35-2h)^2 =0
4h=35-2h
6h=35
solve for h, then the cut squares are hxh.
hen the corners of size x are cut out, the dimensions of the box are
35-2x and 35-2x and x, and the volume is thus
v = (35-2x)(35-2x)x
= 1225x - 140x^2 + 4x^3
dv/dx = 1225 -280x + 12x^2
dv/dx = 0 when x = 5.83333
an open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size from the corners and bending up the sides. what size should be cut out to create a box with the greatest volume? what is the maximum volume?
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