Problem $1($line balancing$)$:

Consider the following process:

Consider the following facts$/$constraints:

$,$ The process is a make$-$to$-$order process

An order for one flow unit is placed exactly every $5$ minutes.

The following workers are available: A$,$ B$,$ C$,$ D$,$ E$,$ F and G$.$ Not all of them need to be employed

in the process but no other worker can be hired.

All other resources can be ignored because they are irrelevant.

The duration of Task $2$ per flow unit depends on the number of workers assigned to the task

according to the formula $32+36/($# workers$).$ For example, if one worker does Task $2,$ its

duration is $32+\frac{36}{1}=68$ minutes; if two workers $($jointly$)$ do Task $2,$ its duration is $32+\frac{36}{2}=50$

minutes; etc.

Tasks $1$ must be performed before all other tasks.

Tasks $2-3$ are performed on the top part of the flow unit and tasks $4-5$ are performed on the

bottom part of the flow unit. As such, tasks $2-3$ can take place at the same time as tasks $4-5.$

Task $6$ can only be once tasks $1-5$ have been completed and is done using a very specialized

machine that only worker $E$ knows how to operate.

Task $7$ does not involve any worker;

All tasks other than Task $2$ and Task $7$ must be done by one worker only;

Task $8$ must follow Task $7$ and Task $9$ must follow Task $8$;Problem $1($line balancing$)$:

Consider the following process:

Consider the following facts$/$constraints:

The process is a make$-$to$-$order process

An order for one flow unit is placed exactly every $5$ minutes.

The following workers are available: A$,$ B$,$ C$,$ D$,$ E$,$ F and G$.$ Not all of them need to be employed

in the process but no other worker can be hired.

All other resources can be ignored because they are irrelevant.

The duration of Task $2$ per flow unit depends on the number of workers assigned to the task

according to the formula $32+\frac{36}{?}($# workers$).$ For example, if one worker does Task $2,$ its

duration is $32+\frac{36}{1}=68$ minutes; if two workers $($jointly$)$ do Task $2,$ its duration is $32+\frac{36}{2}=50$

minutes; etc.

Tasks $1$ must be performed before all other tasks.

Tasks $2-3$ are performed on the top part of the flow unit and tasks $4-5$ are performed on the

bottom part of the flow unit. As such, tasks $2-3$ can take place at the same time as tasks $4-5.$

Task $6$ can only be once tasks $1-5$ have been completed and is done using a very specialized

machine that only worker E knows how to operate.

Task $7$ does not irwolve any worker;

All tasks other than Task $2$ and Task $7$ must be done by one worker only;

Task $8$ must follow Task $7$ and Task $9$ must follow Task $8$;

All workers are paid $$20$ per hour;

The selling price of a flow unit is $$300$;

One worker cannot do more than one task at the same time;

Assume that if two $($or more$)$ workers are in parallel for one task, they are in parallel for all the

tasks they do$.$

Draw a process flow diagram for how you would suggest organizing the process, in order to achieve the

best value for the following performance metrics:

Prolit rate;

Rush order flow time;

Flow rate;

Average labor utilization;

Cost of direct labor;

And provide the value of these metrics for your process flow diagram. Show all your work.