14  Optimization

Q14.1

Use the simplex algorithm to solve the following problem: Minimize \(4x + 2y + z \le 2\) subject to:

\[ 2x + y + z \le 2 \\ x = y + 3z \le 3 \\ x \ge 0, y \ge 0, z \ge 0 \]

Q14.2

In the Morra game, the set of optimal strategies are not changed if a constant is subtracted from every entry of the payoff matrix, or a positive constant is multiplied times every entry of the payoff matrix. However, the simplex algorithm may terminate at a different basic feasible point (also optimal). Compute B <- A + 2, find the solution of game \(B\), and verify that it is one of the extreme points (14.5) - (14.8) of the original game \(A\). Also find the value of game \(A\) and game \(B\).