1. (6 points) Formulating Linear Programs The goal of this question is to formulate problems as linear programs, not solve them. *(a) (2 points) Recall the absolute value function | : |y| := max { y,-y} Show that the constraint is equivalent to two linear inequalities. feb) (4 points) Consider the system kfb) (4 points) Consider the system of linear equations a +b 123 4a + 3b = 234 5a + 4b = 345 This system of equations is clearly not solvable: adding together the first two equations gives 5a +4b = 357, which is different than the value given in the third equation. Instead, we will approximately solve the above problem by minimizing the total absolute value error of the first two equations, aka. la +b-123+14a +3b-234, (I- l is the absolute value function as defined in part a)), while ensuring the third one, 5a + 4b 345 Formulate this as a linear program. Note that the absolute value function is not a linear function