An assembly line is to be designed to operate $11\mathrm{.}9$ hours per day and supply a steady demand of $510$ units per day. Here are the tasks and their performance times:

TASK

PRECEDING TASKS

PERFORMANCE TIME $($SECONDS$)$

a

$34$

TASK

d

PERFORMANCE TIME $($SECONDS

$13$

bcdef

$38$

$46$

$1$

$46$

$8$

$51$

k

PRECEDING TASKS

$18$

b

$26$

g h$,1$

$8$

C

$18$

j$.$k

$58$

$13$

b$.$ What is the workstation cycle time required to produce $510$ units per day?

Workstation cycle time

seconds per unit

c$.$ What is the theoretical minimum number of workstations?

Note: Round up your answer to the next whole number.

Minimum number of workstations