Describes the mathematics and the computer program for solving the problem of optimum bonus management formulated in [A Dynamic] [Model for Optimum Bonus Management], R-1940. The problem of optimum bonus management is treated as a discrete linear control system with a quadratic cost function and solved by using Pontryagin's discrete maximum principle. The state of the system at discrete time is a vector of numbers of men in each of a set of year groups. The system evolves linearly in time under linear controls that are the bonuses paid to the men in a prescribed subset of the year groups. The program solves for the sequence of bonus values that drive given initial state of year groups to a prescribed final state and minimize a sum of quadratic bonus and penalty costs. The program, which consists of a main program and 22 subroutines, is written in FORTRAN IV double precision for the IBM 370-158. 57 pp.