3. (20 points) You have an open position and seek to hire a qualified candidate. In your esti- mation, the Human Resources department is likely to find one candidate each day for each of the next 20 days before your deadline. Because HR cannot always fully appreciate the needs of hiring managers, they advise managers that the probability of a given candidate being exceptional is 2%. The chance that the candidate is merely acceptable is 20%. The chance of the candidate being completely unsuitable is 78%. You cannot hire an unsuitable candidate. If you don't fill the position, you won't be able to get all of the necessary work done. Your preferences can be summarized as: Hiring an exceptional candidate is 5 times better than hiring a merely acceptable one. Hiring an acceptable candidate is 5 times better than not hiring anyone. Use dynamic programming to solve this problem. Be sure to identify the stage, state, avail- able decisions and the recursive relationship that could be used to solve this problem. Your solution should prescribe the best action to take at each stage and state as well as the expected outcome. 3. (20 points) You have an open position and seek to hire a qualified candidate. In your esti- mation, the Human Resources department is likely to find one candidate each day for each of the next 20 days before your deadline. Because HR cannot always fully appreciate the needs of hiring managers, they advise managers that the probability of a given candidate being exceptional is 2%. The chance that the candidate is merely acceptable is 20%. The chance of the candidate being completely unsuitable is 78%. You cannot hire an unsuitable candidate. If you don't fill the position, you won't be able to get all of the necessary work done. Your preferences can be summarized as: Hiring an exceptional candidate is 5 times better than hiring a merely acceptable one. Hiring an acceptable candidate is 5 times better than not hiring anyone. Use dynamic programming to solve this problem. Be sure to identify the stage, state, avail- able decisions and the recursive relationship that could be used to solve this problem. Your solution should prescribe the best action to take at each stage and state as well as the expected outcome