Linear programming question. Any help is appreciated

Consider a problem of the form: min z (x) = max {f_1(x), f_2(x), ..., f_k (x)} S.t. Ax = b (MIN MAX) x greaterthanorequalto 0 where x elementof R^n is the decision variable. A is an m times n matrix, b is in R^m and each f_i is a function from R^n to R. Use appropriate technique to prove that (MINMAX) is equivalent to the following linear program (LP3) min zeta(x, t) = t St. f_i(x) lessthanorequalto t i = 1, ..., k Ax = b x greaterthanorequalto 0 Consider again the linear system in part 4 of last section and the absolute errors. (a) Formulate a (MIN MAX) problem for finding x_1 and x_2 that minimizes the maximum of the absolute errors. (b) Solve the problem. Consider a problem of the form: min z (x) = max {f_1(x), f_2(x), ..., f_k (x)} S.t. Ax = b (MIN MAX) x greaterthanorequalto 0 where x elementof R^n is the decision variable. A is an m times n matrix, b is in R^m and each f_i is a function from R^n to R. Use appropriate technique to prove that (MINMAX) is equivalent to the following linear program (LP3) min zeta(x, t) = t St. f_i(x) lessthanorequalto t i = 1, ..., k Ax = b x greaterthanorequalto 0 Consider again the linear system in part 4 of last section and the absolute errors. (a) Formulate a (MIN MAX) problem for finding x_1 and x_2 that minimizes the maximum of the absolute errors. (b) Solve the