At the beginning of each week, a machine is either running or broken down. If the machine runs throughout the week, it earns revenues of $100. If the machine breaks down during a week, it earns no...

At the beginning of each week, a machine is either running or broken down. If the machine runs throughout the week, it earns revenues of $100. If the machine breaks down during a week, it earns no revenue for that week. If the machine is running at the beginning of the week, we may perform maintenance on it to lessen the chance of a breakdown. If the maintenance is performed, a running machine has a .4 chance of breaking down during the week; if maintenance is not performed, a running machine has a .7 chance of breaking down during the week. Maintenance costs $20 per week. If the machine is broken down at the beginning of the week, it must be replaced or repaired. Both repair and replacement occur instantaneously. Repairing a machine costs $40, and there is a .4 chance that the repaired machine will break down during the week. Replacing a broken machine costs $90, but the new machine is guaranteed to run throughout the next week of operation. Use dynamic programming to determine a repair, replacement, and maintenance policy that maximizes the expected net profit earned over a four-week period. Assume that the machine is running at the beginning of the first week.