Lemon Scooters assembly process is a simple line flow with three steps: deck assembly, wheel assembly, and packaging. Two types of scooters are made in this line, the Lemon$-$Ultra and the Lemon$-$Street.

The market demand for Lemon$-$Ultra is the same as the market demand for Lemon$-$Street.

In the Deck Assembly step, processing time is $0\mathrm{.}5$ minute per unit for both types of scooters. Currently the production batch size at the Desk Assembly is $50$ units for Lemon$-$Ultra and $100$ units for Lemon$-$Street. The set$-$up time for each batch of Lemon$-$Ultra is $10$ minutes and $30$ minutes for Lemon$-$Street.

In the Wheel Assembly step, processing time is $1$ minute per unit for both types of scooters. Currently the production batch size at the Wheel Assembly is $100$ units for both types of scooters. The wheel assembly tool needs to be replaced before processing each batch. The replacement time is $20$ minutes for both types of scooters $($this is the set$-$up time for each batch$).$

The Packaging step processes scooters unit by unit $($there is no batching in the Packaging step$).$ It takes $0\mathrm{.}5$ minute per unit for both types. $($There is no difference to package either type of scooters.$)$

The plant operates $24$ hours a day, $7$ days a week.

Question $10.$ Which of the following is a plausible sequence of production batches between Ultra and Streetmodels at Deck Assembly station that matches the product mix demanded by the market $($i$.$e$.,$characterize a repeating cycle that yields the desired product mix at Deck Assembly$)?$

a$.$ Ultra, Street, Street, $....$

b$.$ Ultra, Ultra, Ultra, Ultra, Street, $....$

c$.$ Ultra, Ultra, Street, $....$

d$.$ Street, Street, Street, Ultra, Ultra, $....$

Question $11.$ Which of the following is a plausible sequence of production batches between Ultra and Street models at Wheel Assembly station that matches the product mix demanded by the market $($i$.$e$.,$ characterize a repeating cycle that yields the desired product mix at Wheel Assembly$)?$

a$.$ Ultra, Street,....

b$.$ Ultra, Ultra, Street, $....$

c$.$ Street, Street, Ultra, $....$

d$.$ Ultra, Street, Street, $....$

Question $12.$ What is the production capacity for Deck Assembly in scooters per hour? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Question $13.$ What is the production capacity for Wheel Assembly in scooters per hour? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Question $14.$ What is the capacity for packaging in scooters per hour? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Question $15.$ Suppose all three steps process at the bottleneck rate that you calculated $($in other words, the non$-$bottleneck steps slow down and process at the rate of the bottleneck$).$ Assuming that at

time t$=0,$ there is a finished batch from Wheel Assembly and just arrived the Packaging station. Thus, the WIP buffer in front of Packaging station starts a maximum level of $100$ units at t$=0$

and decreases at the bottleneck rate. What is the average time in hour that a scooter is spent in the WIP buffer? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Question $16.$ In order to improve the system capacity, the management has studied the wheel assembly step. After improving the assembly method, the replacement time for the assembly tool reduces from $20$ minutes to $10$ minutes, whereas the processing time per unit reduces from $1$ minute to $0\mathrm{.}5$ minutes. What is the system capacity in scooters per hour after this improvement? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$ Hint: You need to check which step is the new bottleneck.