Draw a gantt chart, Basic Statistics

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Consider the Kristen Cookie Company case.

From the note:
Wash&Mix: 6 mins per order (max 3 dozen)
Dish up: 2 mins per dozen
Set up timer: 1 min per dozen
Bake: 9 mins per dozen
Cool off: 5 mins per dozen
Pack: 2 mins per dozen
Accept payment: 1 min per order

Assume that
• the roommate is sick so Kristen has to set the timer, pack and accept payment herself (on top of her usual tasks)
• all orders are for one dozen cookies.
• acustomer places an order every 12 minutes (that is the first customer places an order in the beginning of the 1st minute, the second places an order at the beginning of the 13th minute, etc...).
• customers are there to pay for the orders as soon as they are completed.

(1) What is the cycle time?
(2) What is the average number of orders that are being processed at one moment in time (we say that an order is "being processed" if it has been placed but has not yet been completed and paid for)?
(3) Draw a Gantt chart to illustrate this setting (you may use the blank chart on the next page). If possible, use different colors to represent successive orders during the first 75 minutes.
Also, we make the following assumptions so that everyone gets the same Gantt chart:
1. If at some point in time there are multiple steps that Kristen can do, she always gives priority to the task on the newest order.
2. When necessary, she can break tasks into two, e.g., pack for one minute then do something else, then come back to finish packing for another minute.

Then answer the following questions:
(a) Suppose Kristen starts working at 8pm. What is the completion time of the first 4 orders?
(b) Compute the difference between the completion times of two successive orders (that is, completion time of the second order minus completion time of the first order, completion time of the third order minus completion time of the second, etc.).
(c) Compute the average of the 3 numbers you obtained in (b).
Hint: if your chart is correct, your answer in (c) should be the same as in (1).

Please show all your computations.


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