# Continuous version of rod cutting problem

This is an attempt to extend an idea from Computer Science.. the dynamic programming based solution of the rod cutting problem (given a rod of an integral length and an array of prices for each integral value of the length, find the optimal cuts that maximize profit). Thinking about it made me wonder.. what if we were not constrained to cut the rod at integral values, but could cut it any where we liked (fractional lengths are possible). Further, lets say that instead of a table of prices corresponding to the integral lengths, we are given a continuous (monotonically increasing, tapering) function that represents the value of the rod at different lengths. For example, for a rod of length 1, the value function might be given by the CDF of a beta distribution. Now, we want to find the number of cuts that we should make and at what values to optimize the total value. Has any one heard of such a problem (I couldn't find any thing online)?

• – D.W.
Oct 11 '20 at 20:54