Problem $5$: Figurine Co$.$

Figurine Co$.$ buys pre$-$cut wooden blocks and makes wooden figurines out of them. The process consists of two steps. First, the Carving step carves the wooden blocks into figurines. Second, the Finishing step polishes and paints these figurines. The process flow diagram is given below:

$9$

It takes $10$ minutes to process a figurine at the Carving step and another $10$ minutes to process it at the Finishing step. Currently, there are two workers, one for each step, and they work $8$ hours in a day. Assume that both workers always have units to work on; hence, they are never idle.

The owner of the company is planning to hire a third worker to increase production capacity. This worker will spend the first $4$ hours of the day at the Carving step $($working parallelly with the existing worker$)$ and the last $4$ hours of the day at the Finishing step $($working parallelly with the existing worker$).$ Suppose the new worker will also take $10$ minutes to carve and $10$ minutes to finish a figurine.

Wooden figurines are always in high demand. Assume that this will be a capacity$-$constrained system even with three workers. Also assume that there are always enough raw materials available, and all three workers always have units to work on; hence, they are never idle.

$22.$ Under the current system with only two workers, how many completed units $($i$.$e$.,$ units that have undergone both the carving and the finishing steps$)$ does Figurine Co$.$ manufacture in an $8-$hour workday? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

$23.$ What will be the number of completed units manufactured in an $8$ hour workday under the new system with three workers? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

$24.$ With three workers, what is the maximum number of units that will accumulate in the WIP buffer between the Carving and the Finishing steps during a day? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

$25.$ With three workers, how long $($in hours$)$ does an average unit spend in the WIP buffer between the two steps? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$