(25 pts) Dr. Rosemary Seva the incoming Dean of Gokongwei College of Engineering will have to appoint her Associate Dean. She has to identify a number of possible candidates. Each candidate i has an efficiency rating of r. The probability of candidate i accepting the jth offer to be the Associate Dean (assuming the first j-1 offers to other candidates were declined) is denoted by p. Dr. Seva wants to identify her strategy in offering the position to the possible candidates that would maximize the expected efficiency rating. a. (2 pt.) Define the Stage, State, and Decision for this problem if this will be solved using Dynamic Programing. Assume backward pass. b. (3 pts.) Formulate the return function and recursive function for the last stage. c. (5 pts.) Formulate the general return function, recursive function, transition function applicable to the first stage up to the second to the last stage. d. (15 pts.) Assume that Dr. Seva is considering four candidates for Associate Dean position. Her choices include the current Associate Dean - Engr. Efren Dela Cruz. Her other choices are Dr. Jonathan Dungca, Engr. Antonette Roque, and Dr. Vergel Bungay. Given the four possible candidates, Dr. Seva is planning to individually talk to at most 3 of them and offer the position one at time. Each of these candidates has a perceived efficiency rating on their first year as Associate Dean. The perceived efficiency rating is measured by the following criteria: (1) familiarity with the responsibilities; (2) length of service with GCOE; and (3) the motivation brought about by how the offer was made. The efficiency rating (based on the first two criteria) on a scale from 1 (lowest) to 10 (highest) are given in the table below. Candidates Rating Dela Cruz 10 Dungca 7 Roque 8 Bungay These perceived efficiency ratings will change if the third criterion is considered. The above efficiency ratings of Engr. Dela Cruz and Engr. Roque will be reduced to 6 and 7, respectively if they were not given the top priority. The efficiency ratings of Dr. Dungca and Dr. Bungay will increase to 8 and 5, respectively if they were not given the top priority. The probabilities that each candidate with accept the offer to be the Associate Dean are shown in table. Candidate Offer Dela Cruz Dungca Roque Bungay 0.6 0.9 0.8 1.0 2nd 0.3 06 0.7 0.8 3 0 0.4 0.3 0.5 Using Dynamic Programming, determine how Dr. Seva will offer the position to possible candidates that will maximize the expected efficiency rating for their first year as Associate Dean. No need to formulate the return function, recursive function, and transition function in every stage.