2. Consider the following optimization problem 

maximize Z = 2|x|−y

subject to x−y ≤ 6

2x + y ≥−3

with x ∈R, y ≤ 0

(a) Is this problem an LP problem in its current form? Explain your answer.

(b) Convert this problem to an (equivalent) LP problem of the following form:

Maximize Z = cTx

subject to Ax = b

with x ≥ 0, x ∈Rn

where c ∈Rn, 0 ≤ b ∈Rm and A is an m × n matrix. Explain every step you make. In particular, if you introduce new variables explain why this is needed.