Problema Solution
A gutter is to be made from a metal sheet which is 300mm wide, by bending up equal widths along the edges into vertical positions. What dimentions will give the largest capacity??
Answer provided by our tutors
volume = length * width * height
we let length = 1mm since only the width and height will be affected by bending along the edges
let 'x' represent the amount of bend along a given edge, then '300-2x' represents the width of the gutter after bending and 'x' represents the height of the gutter
Volume = 1 * x * (300-2x)
Volume = -2x^2 + 300x
Volume = -2(x-75)^2 + 11250
we minimize -2(x-75)^2 by choosing x=75
300 - 2*75 = 150
the dimensions giving the largest capacity will be a height of 75mm and a width of 150mm