Rita Gibson Appliances wants to establish an assembly line to manufacture its new product, the

Mini$-$Me Microwave Oven. The company would like to organize the work as efficiently as possible. A list of tasks, task

times, and precedence requirements are given in the following table.

Task Precedence Relationships Task time $($in minutes$)$

A $------6$

B A $4$

C B $6$

D B $5$

E C$,$ D $4$

F E $5$

a$.$ Draw the precedence diagram. If the operation manager assigns one employee per task, what is $($are$)$ the

bottleneck task$($s$)$ of the assembly line and the hourly capacity of the line $($in units per hour$)?$

b$.$ What are the minimum and maximum cycle times? What hourly range of theoretical output is possible for this

assembly line?

c$.$ If the company wants to produce a Mini$-$Me Microwave Oven every $10$ minutes $($i$.$e$.,$ cycle time$),$ what is the

theoretical minimum number of employees needed? Balance the assembly line $($i$.$e$.,$ assign tasks to workstations$).$

How many employees should be hired $($i$.$e$.,$ the actual number of employees$)?$

d$.$ Calculate the efficiency of the assembly line. How many ovens can be assembled in an eight$-$hour shift?