2 Operations Research 1 Due Date: 4 May 2016 Please submit your work to the class coordinator or the assistants! 1. Consider the following puzzle. You are to pick out 4 three-letter \"words\" from the following list: DBA DEG ADI FFD GHI BCD FDF BAI For each word, you earn a score equal to the position that the word's third letter appears in the alphabet. For example, DBA earns a score of 1, DEG earns a score of 7, and so on. Your goal is to choose the four words that maximize your total score, subject to the following constraint: The sum of the positions in the alphabet for the first letter of each word chosen must be at least as large as the sum of the positions in the alphabet for the second letter of each word chosen. Formulate an IP to solve this problem. 2. Gama Press sells textbooks to UGM students. Gama Press has two sales reps available to assign to the A-G complex area. The number of students (in thousands) in each complex area is given in the figure. Each sales rep must be assigned to two adjacent complex area. For example, a sales rep could be assigned to A and B, but not A and D. Gama Press's goal is to maximize the number of total students in the states assigned to the sales reps. Formulate an IP whose solution will tell you where to assign the sales reps. 3. Coach Night is trying to choose the starting lineup for the basketball team. The team consists of seven players who have been rated (on a scale of 1 poor to 3 excellent) according to their ball-handling, shooting, rebounding, and defensive abilities. The positions that each player is allowed to play and the player's abilities are listed in the table. The five-player starting lineup must satisfy the following restrictions: - At least 4 members must be able to play guard, at least 2 members must be able to play forward, and at least 1 member must be able to play center. - The average ball-handling, shooting, and rebounding level of the starting lineup must be at least 2. - If player 3 starts, then player 6 cannot start. - If player 1 starts, then players 4 and 5 must both start. - Either player 2 or player 3 must start. Given these constraints, Coach Night wants to maximize the total defensive ability of the starting team. Formulate an IP that will help him choose his starting team. Player Position 1 2 3 4 5 6 7 G C G-F F-C G-F F-C G-F Ball Handling 3 2 2 1 3 3 3 Shooting Rebounding Defense 3 1 3 3 3 1 2 1 3 2 3 3 2 2 3 2 2 1 3 3 1