You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the following dimensions will give you the greatest volume?
Suppose you cut squares have the side lengths x then we have length of base box=20-2x width of base box=30-2x height of box=x volume of the box V=x(20-2x)(30-2x) V=600x-100x^2+4x^3 then dV/dx=600-200x+12x^2 set that to zero 600-200x+12x^2=0 apply quadratic formula x=approx12.97 or 3.92 since you want in whole numbers so x=13 or x=4 so if x=13 then V= -312 but negative number doesn't make a sense so we ignore that if x=4 then v=1056 this is the greatest volume the dimensions are length of a box base=12 width of a box base=22 height of box =4 did u get it ?
