$.($Assign Tasks to Workers$)$ Consider the following six tasks that must be assigned to four workers on a conveyor$-$paced assembly line $($i$.$e$.$ a machine$-$paced line flow$).$ Each worker must perform at least one task.

Time to Complete Task $($seconds$)$

Task $130$

Task $225$

Task $335$

Task $440$

Task $515$

Task $630$

The current conveyor$-$paced assembly line configuration assigns the workers in the following way:

$$ Worker $1$: Task $1$

$$ Worker $2$: Task $2$

$$ Worker $3$: Tasks $3,4$

$$ Worker $4$: Tasks $5,6$

a$.$ What is the capacity of the current line?

b$.$ Now assume that tasks are allocated to maximize capacity of the line, subject to the conditions that $(1)$ a worker can only perform two adjacent operations and $(2)$ all tasks need to be done in their numerical order. What is the capacity of this line now?

c$.$ Now assume that tasks are allocated to maximize capacity of the line and that tasks can be performed in any order. What is the maximum capacity that can be achieved?