The branching part of the branch and bound algorithm that Solver uses to solve integer optimization models means that the algorithm [a] creates subsets of solutions through which to search [b] searches through only a limited set of feasible integer solutions [c] identifies an incumbent solution which is optimal [d] uses a decision tree to find the optimal solution 2. The LP relaxation of an integer programming (IP) problem is typically easy to solve and provides a bound for the IP model. [a] True [b] False

Insufficient Overlapping Subproblems and the Principle of Optimality (Optimal Substructure) are both acceptable queries for dynamic programming. Consider All-Pairs Shortest Paths as an illustration of the difficulty in achieving these two requirements.

8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonablo time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutions

4. Describe a dynamic programming approach for a modified knapsack problem in which up to 3 copies of each of the n items can be selected