Texts: Optimization Problem Using Branch and Bound Method and Integer Linear Programming
1. One Man's Trash
You're at a yard sale and have spied four crates of goods. You've estimated the value of each crate. Crate A is valued at $5000, Crate B at $600, Crate C at $3500, and Crate D at $6000. The owner has no idea what these are worth and is selling them for $24, $76, $43, and $754 respectively. You realize that you can purchase these crates and sell them at a much higher markup. However, you walked here and can only buy what you can carry on your person. You have $800 and can carry an estimated 85 pounds (you may change this to kilograms if you feel like you are stronger than this). Crate A weighs 75.5 pounds, Crate B weighs 2.7 pounds, Crate C weighs 3.3 pounds, and Crate D weighs 6.7 pounds. Fortunately, you are taking this class and have identified this as an integer programming problem.
1. Write the above as an integer linear program (think carefully about what values the variables can take).
2. Use the branch and bound algorithm to find the optimal solution, explaining your choices for which variables to branch on and where to prune the tree.
3. Draw the branch and bound tree for your solution.
(Hint: Note that you should use linprog to solve the relaxed linear program, initially with your variables constrained between 0 and 1)
2. Max Flow
Compute the maximum possible flow from source (node 0) to sink (node 5) for the following graph. Also, identify the minimum cut:
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