theory - Continuous version of rod cutting -

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this might not question forum, attempt extend idea computer science.. dynamic programming based solution of rod cutting problem (given rod of integral length , array of prices each integral value of length, find optimal cuts maximize profit). asked question implementation of rod cutting problem here yesterday. thinking made me wonder.. if not constrained cut rod @ integral values, cut liked (fractional lengths possible). further, lets instead of table of prices corresponding integral lengths, given continuous (monotonically increasing, tapering) function represents value of rod @ different lengths. example, rod of length 1, value function might given cdf of beta distribution. now, want find number of cuts should make , @ values optimize total value. has 1 heard of such problem (i couldn't find thing online)?


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