Problem 1 parts a and b)

(a) Complete the argument started in Lecture 1: prove that the optimization problems (P1) minimize 2:le wi(aT:Eb)+ (P2) minimize 2:le tug-ti '5' subject to 23:0 subject to ytO afybi 0, i = 1, . . . , k, are equivalent by showing that o for every feasible solution LI) of (P1), there exists a feasible solution (y,t) of (P2) With f2,0(y9t) S f1,0($)= and o for every feasible solution (y,t) of (P2), there exists a feasible solution a: of (P1) With f2,0(y9t) Z f1,0($)- (Here, flag and 11210 denote the objective functions of (P1) and (P2), respectively.) (b) Derive a linear program equivalent to minimize \"An: b\"DO + p||$||1, Where p Z 0. You don't need to provide an equivalency argument in your written solutions, but do one on your own to make sure your linear program is correct (in particular, the assumption p Z 0 should be relevant to your argument)