An assembly

$-$

line process has six tasks, as listed in the table below: Task time Task

$1$

$1$

$5$

$$min Task

$2$

$8$

$$min Task

$3$

$1$

$7$

$$min Task

$4$

$2$

$0$

$$min Task

$5$

$6$

$$min Task

$6$

$2$

$4$

$$min Four workers

$($

S

$1$

$,$

$$S

$2$

$,$

$$S

$3$

$,$

$$and S

$4$

$)$

$$are staffed to this assembly line, and the assignment of tasks to each worker is as follows:

$$

$$S

$1$

$$does Task

$1$

$.$

$$

$$S

$2$

$$does Tasks

$2$

$$and

$3$

$.$

$$

$$S

$3$

$$does Tasks

$4$

$.$

$$

$$S

$4$

$$does Tasks

$5$

$$and

$6$

$.$

$$For the following questions, we assume that the process is operating at full capacity.

$($

a

$)$

$$Which worker is the bottleneck of the process? What is the process capacity in

$[$

units

$/$

hour

$]$

$?$ Assume a wage rate of $$18$ per hour. What is the direct labor cost in $[$$$/$unit$]?$