Q$1.($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. Task $1$ Task $2$ Task $3$ Task $4$ Task $5$ Task $6$ Time to Complete Task $($seconds$)302535401530$ 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?