A production facility has N machines. If a machine starts up correctly in the morning, it renders a daily revenue of 18. A machine that does not start up correctly, needs to be repaired. A visit by a repair man costs $ per day and he repairs all broken machines on the same day. The repair cost is a lump-sum amount and does not depend on the number of machines that is repaired. A machine that has been repaired always starts up correctly the next day. The number of machines that start up correctly the next day depends on the number of properly working machines at present day and is governed by the probability distribution given in the table below, where m stands for the number of (presently) working machines and n stands for the number of ones that would start up correctly the next day. The goal for the facility manager