A toy shop is making a robot that has two major parts. The first part is produced in assembly line ACE $($which has machines A$,$ C$,$ and E$),$ and the second part is produced in assembly line BDF $($which has machines B$,$ D$,$ and F$).$ Then these two parts are assembled by Machine G$.$

The productivity of each machine is given below.

Productivity

Machine

$($units$/$hour$)$

A

$16$

B

$20$

C

$13$

D

$10$

E

$15$

F

$18$

G

$30$

H

$28$