1. In Rock-Paper-Scissors II: Judgment Day, rock crushes scissors by a margin of 3 (i.e, rock wins $3 and scissors loses $3), scissors cuts paper by a margin of 2, and paper covers rock by a margin of 1. How should you play?

2. Use the revised simplex algorithm to solve the following LP:

Maximize 3x₁ + 4x₂ subject to
x₁+2x₂ ≤ 11
4x₁+3x₂ ≤ 29
x₁, x₂ ≥ 0

3. Exercise 4.8 (Hint: The determinant of an n x n matrix A is a signed sum of all possible n-fold products of entries in A, where no two entries in any product belong to the same row or same column.)

4. Use the primal-dual algorithm to compute the shortest path from s to t in the directed graph given in Example 5.1, replacing edge weight w with 7-w.

5. Exercise 5.3