A hiker plans to go on a camping trip. There are 5 items the hiker wishes to take with her, but together they exceed the 60-lb weight limit she feels she can carry. To assist herself in the selection process, she has assigned a value to each item. Item Weight (lb) Value 1 52 100 2 23 60 3 35 70 4 15 15 5 7 15 (a) Build a binary integer programming model and use a computer to solve it. (b) Use the branch and bound method to solve this problem step by step. (Hint: Each item is either chosen or not, you should add more constraints to the original BIP model, then solve this relaxed BIP model as the first linear programming model). You should state clearly each subproblem (a linear programming model), its upper bound and lower bound, its optimal solution, and its further branches (subproblems), etc. (c) Draw a diagram (a tree) to show all subproblems (nodes), branches, etc.