2. (6 pts) Consider the integer program below: max f (w, x, y,z) = 2w+3x+ 2y+4z subject to: 2w+3y+5z $150 W,1,y,220 4w+7x+3ys 420 w, x, y, z integers Introduce (a) new variable(s) as needed and add additional linear constraints to specify the logical condition that "if x is less than or equal to 12, y must be less than or equal to x." (There's nothing important about the exact maximization problem above.)