Formulate a binary program to solve the following problem: a) You have 25 people in your running club. You are sponsoring 5 races. Each person runs 4 races and volunteers at the water station at one race. You need an equal number of people running each race. Everyone tells you their preference for running each race, on a scale of 1 (good) to 10 (bad). Your goal is to maximize overall satisfaction. Formulate a mathematical program that could help you solve this problem. b) Update your solution to include the constraint that every person gets to specify 2 favorite races, and they must get to run in at least one of them. c) Update your answer to include the constraint that Amy and Oliver cannot work at the water station for the same race. d) Update your solution to add in the constraint that Amy's satisfaction(measured by the sum of her values for all the races she's been assigned) cannot be better than anyone else's satisfaction. e) How would you modify your model to say "Amy can only run the St. Patrick's Day 5k if Tim also runs it