(20 points) Write an integer program for the following wedding planning problem. Your task is to decide which people to invite, subject to some constraints. a) You and your partner have identified a list of 300 contenders, but your budget only allows for 150 guests. Write a constraint that imposes this budget condition. b) For each of the 300 contenders, you have given a numeric score (from 1 to 5) quantifying their desirability to have at the wedding. Your goal is to maximize the sum of desirability scores of invited guests. c) If you invite your Aunt Sarah, then you must also invite your crazy Uncle Steve (and vice versa). d) Your friends Jacob and Ellen are bitter exes, so you should not invite both of them. e) Your co-worker Tony does not know any of your family. So, if you invite him, then you should also invite one or more of your other coworkers (Mary or Bob) so he has someone to talk with. (Meanwhile, Mary and Bob know your sister who is definitely coming.) Below is a table showing the first 7 guests from your list of 300 contenders. # (Possible) Guest Name 1 Aunt Sarah 2 Uncle Steve 3 Jacob 4 Ellen 5 Tony 6 Mary 7 Bob As mentioned above, be sure to declare all relevant indices, parameters, sets, variables, etc that you use. Do not solve the IP. (20 points) Write an integer program for the following wedding planning problem. Your task is to decide which people to invite, subject to some constraints. a) You and your partner have identified a list of 300 contenders, but your budget only allows for 150 guests. Write a constraint that imposes this budget condition. b) For each of the 300 contenders, you have given a numeric score (from 1 to 5) quantifying their desirability to have at the wedding. Your goal is to maximize the sum of desirability scores of invited guests. c) If you invite your Aunt Sarah, then you must also invite your crazy Uncle Steve (and vice versa). d) Your friends Jacob and Ellen are bitter exes, so you should not invite both of them. e) Your co-worker Tony does not know any of your family. So, if you invite him, then you should also invite one or more of your other coworkers (Mary or Bob) so he has someone to talk with. (Meanwhile, Mary and Bob know your sister who is definitely coming.) Below is a table showing the first 7 guests from your list of 300 contenders. # (Possible) Guest Name 1 Aunt Sarah 2 Uncle Steve 3 Jacob 4 Ellen 5 Tony 6 Mary 7 Bob As mentioned above, be sure to declare all relevant indices, parameters, sets, variables, etc that you use. Do not solve the IP