Consider the Kristen$$s Cookie Company $($KCC$)$ case when both you and your roommate are working. Suppose that the sequence of processing stages stays the same, but the duration of some of the process steps has changed. The sequence of steps and their duration are as follows:

Mixing $6$ minutes of labor time for $1$ dozen cookies:

$7$ minutes of labor time for $2$ dozens of the same type of cookies;

$8$ minutes of labor time for $3$ dozens of the same type of cookies;

Spooning $3$ minute of labor time per dozen cookies;

Baking $15$ minutes of oven time per dozen cookies $(1$ minute of labor time

to set up and load the oven followed by $14$ minutes of baking;

Cooling $4$ minutes;

Packing $2$ minutes of labor time per dozen cookies;

Payment $2$ minutes of labor time per order.

You will mix and spoon; your roommate will set up and load the oven, pack, and accept payment. Your roommate will also unload the oven but we shall assume that this activity consumes negligible time and can be performed in the middle of doing something else. Furthermore, assume that three identical ovens are available for your use. Answer the following questions on the basis of the above information.

B$.$ Suppose that each customer order is for two dozen cookies of the same type.

$($i$)$ What would be the bottleneck and the system capacity $($in dozens per hour$)?(3$ points$)$

$($ii$)$ What is the cycle time $($in minutes$)?(2$ points$)$

$($iii$)$ What is the rush order throughput time $($in minutes$)?(2$ points$)$

$($iv$)$ What is the impact on rush order throughput time $($Does not change? Increases? Decreases?$),$ if only two ovens are working? Show work. $(2$ points$)$