The Lumber Optimizer is a little like quantum physics. But don’t be intimidated. The Lumber Optimizer is EZ! Since the longer the diagonal the more weight the shelf can bear, the basic idea is that in order to extract the full value of the lumber, we must exploit the full length of the lumber (L). But like quantum physics, this means that there can only be a finite number of solutions of identical diagonals (n) having an outer depth of d2 that can be extracted from the lumber. Given the constraints of L, w, d2 -- and even the width of the cutting blade --the Lumber Optimizer determines all the possible number of diagonals (n) that can be extracted.
The requirement that we utilize the entire length of the lumber with n identical diagonal pieces means that our solution will only involve discrete angles that the diagonal makes with the wall.
After presenting the user with an enumerated list of these n possibilities (next screen), the LumberOptimizer prompts the user to select from one of these options. To aid the user in this selection, the maximum number of diagonals having an angle less than or equal to 45 degrees will be indicated. We call this n, n_45. Using n_45 as a reference, the user may decide to go with extracting fewer diagonals from the length L of lumber (n smaller and also corresponding to a smaller θ and therefore a greater load bearing capacity), or with more diagonals (n larger, but have a larger θ and therefore a lower load bearing capacity).