Linear programming & reductions problem in Algorithm, Show, proof, or Formulating Linear Programs. Don't solve or write code for both (a) & (b)

. E in Formulating Linear Programs The is to not solve the goal of this question formulate problems as linear programs, (a) (2 points) Recall the absolute value function | | |y = maxY, -Y } Show that the constraint and Te Au T> > fel Rity is equivalent to two linear inequalities. b) (4 points) Consider the system of linear equations: don Soly a +b = 123 Sho near Program 4a + 3b = 234 5a +4b = 345 and (b) This system of equations is clearly not solvable : adding together the first two equations gives a +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. ite CA 't I IV proof of formulate . (a +b 123) + |4a + 3b 234), (| | 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 . E in Formulating Linear Programs The is to not solve the goal of this question formulate problems as linear programs, (a) (2 points) Recall the absolute value function | | |y = maxY, -Y } Show that the constraint and Te Au T> > fel Rity is equivalent to two linear inequalities. b) (4 points) Consider the system of linear equations: don Soly a +b = 123 Sho near Program 4a + 3b = 234 5a +4b = 345 and (b) This system of equations is clearly not solvable : adding together the first two equations gives a +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. ite CA 't I IV proof of formulate . (a +b 123) + |4a + 3b 234), (| | 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