Problem 4: Suppose you're managing a consulting team of expert computer hackers, and eadh week you have to choose a job for them to undertake. Now, as you can well imagine, the set of possible jobs is divided into those that are low-stress (eg, setting up a Web site for a class at the local elementary school) and those that are high-stress (e.g., protecting the nation's most valuable secrets, or helping a desperate group of Cornell students finish a project that has something to do with compilers). The basie question, each week, is whether to take on a low-stress job or a high-stress job. If you select a low-stress job for your team in week i, then you get a revee of 0 dollans if you select a high-stress job, you get a revenne of h, >0 dollars. The catch, however, is that in order for the team to take on a high-stress job in week i, it's required that they do no job (of either type) in week i -1; they need a full week of prep time to get ready for the crushing stress level On the other hand, it's okay for them to take a low-stress job in week i even if they have done a job (of either type) in week i -1. So, given a sequence of n weeks, a plan is specified by a choice of "low-stress," "high-stress," or "none" for each of the n weeks, with the property that if "high-stress is chosen for week i >1 then "none" has to be chosen for week i -1. (It's okay to choose a high-stress job in week 1.) The value of the plan is determined in the natural way: for each i, you add I, to the value if you choose low-stress in week i, and you add h, to the value if you choose "high-stress" in week i. (You add 0 if you choose "none in week i.) The problem. Given sets of values 2., and h,h.ha, find a plan of maximum value (Such a plan will be called optimal.) Example. Suppose n = 4, and the values of I. and h, are given by the following table. Then the plan of maximum value would be to choose "none in week 1, a high-stress job in week 2, and low-stres jobs in week 3 and 4. The value of this plan would be 0 + 50 + 10 + 10 = 70. Week 1 Week 2 Week 3 Week 4 10 10 10 50 (a) Show that the following algorithm does not correctly solve this problem, by giving an instance on which it does not return the correct