Task time estimates for the new Japanese Cheesecake at YallaCake are shown below. The demand for the cakes is $1,800$ units per $24-$hour. Omar, the bakery$$s manager, is trying to improve the productivity of YallaCake by hiring more employees.

Task

Time $($sec$)$

Predecessors

A

$26$

None

B

$32$

None

C

$19$

None

D

$12$

A$,$B

E

$28$

B$,$C

F

$15$

D$,$E

G

$22$

F

H

$28$

F

a$)$ What is the cycle time for this operation?

b$)$ What is the theoretical minimum number of employees needed? c$)$ Is the number of employees in $($b$)$ realizable? If not, what is the actual number of employees needed?

d$)$ Based on $($c$),$ what is the efficiency of the line and the total idle time per cycle?