How would you decompose the problem of fast subroutine

Question

Problems:

Consider the following LP problem

                      min   c^Tx+d^Tz
                       s.t.   Ax+Dz≤b
                               Fx≤f
                               z≥0

(a) Suppose we have a very fast routine to solve the problems of the form

                        min  h^Tx
                         s.t. Fx≤f

for arbitrary vectors . How would you decompose the problem above the take advantage of such fast subroutine?

(b) Suppose we have a very fast routine to solve problems of the form

                        min d^Tz
                         s.t. Dz≤h
                                z≥0

for arbitrary vectors . How would you decompose the problem above the take advantage of such fast subroutine?