$($Process Improvement$)$ There are four activities involved in baking a cake: mixing, baking, cooling, and decorating. The activities must be performed in this order. The processing time for each activity is as follows:

Activity Processing Time $($minutes per cake$)$

Mixing $8$

Baking $25$

Cooling $15$

Decorating $10$

The demand rate is $3$ cakes per hour. Currently, we have worker A in charge of mixing, worker B in charge of baking, and worker C in charge of cooling and decorating.

a$.$ If each worker is paid $$12$ per hour, what is the cost of direct labor associated with baking one cake?

b$.$ What is the labor content $($in minutes$)$ associated with baking one cake?

c$.$ What is the total idle time $($in minutes$)?$

d$.$ What is the average labor utilization?

e$.$ What is the takt time $($in minutes$)?$

f$.$ What is the target manpower for the given demand rate?

g$.$ If we balance the line by moving decorating to worker B$,$ what is the average labor utilization?

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