10. You're trying to run a large computing job in which you need to simulate a physical system for as many discrete steps as you can. The lab youre working in has two large supercomputers (which we'll call A and B) which are capable of processing this job. However, you're not one of the high priority users of these supercomputers, so at any given point in time, you're only able to use as many spare cycles as these machines have available. Here's the problem you face. Your job can only run on one of the machines in any given minute. Over each of the next n minutes, you have a "profile" of how much proces sing power is available on each machine. In minute i, you would be able to run a> 0 steps of the simulation if your job is on machine A, and bt> 0 steps of the simulation if your job is on machine B. You also have the ability to move your job from one machine to the other; but doing this costs you a minute of time in which no processing is done on your job. So, given a sequence of n minutes, a plan is specified by a choice of A, B, or move" for each minute, with the property that choices A and