(Solved): Linear Programming a) Write the optimization problem "maximize \( 2 x+3 y \) subject to \( |x|+|y| \ ...

a) Write the optimization problem "maximize \( 2 x+3 y \) subject to \( |x|+|y| \leq 1 \), where \( x, y \in \mathbb{R} \) " as a linear program. b) Write the optimization problem "minimize \( |x|+|y| \) subject to \( 2 x+3 y \geq 1 \), where \( x, y \in \mathbb{R}^{\prime \prime} \) as a linear program. (Hint: first phrase it as minimizing \( z \), where \( z \geq|x|+|y| \). )