Complete homework problems 1 & 2. (Extra practice problems for TSP are on the last page.) The following stories are fictional and do not depict any actual events. 1. "Other Margaret" is riding her bike around Raleigh again. She has perfected her utility function that determines the cost of trips between locations based on distance, grade, and scenery. The costs between Margaret's desired destinations are given below; Location 1 is her home so she must start and end there. 2 3 4 5 6 From 1 - 10 16 15 10 6 To 3 5 10 - 13 8 7 2 5 - 10 8 4 15 4 16 3 8 - 13 15 5 16 14 3 5 - 14 6 16 5 8 15 8 - (a) Using branch and bound, find the optimal schedule that minimizes her travel. Do not use CUCA as an upper bound. (b) Use CUCA to find 3 different schedules and the corresponding costs. 2. "Other Margaret" has just realized that her beautiful cost matrix has one flaw, she forgot to account for the toll between Location 6 and her house (yes, absurdly they even charge cyclists)! Being a poor graduate student, she is unable to pay the toll for her bicycle. Travel between Locations 1 and 6 is not feasible. What is her optimal schedule now? Do not use CUCA as an upper bound