CASE: Kristen’s Cookie Company
Q1: How long will it take you to fill a rush order?
It depends on the number of dozens that the rush order requires. Assume that the order requires x dozen(s) (x∈N*) of orders, then the time of filling that order is (16+10x) minutes (assume that this order requires only one flavor). Firstly we consider the situation of a 1 dozen order. The all steps – washing and mixing ingredients (6min), spooning the cookies (2min), putting the cookies in the oven and setting the oven (1min), cooling down the cookies (5min), packing them (2min), and finally accept the payment (1min) – will take 6+2+1+9+5+2+1=26 minutes. Secondly, we consider the situation of a 2dozens order (seen in the Gantt chart followed). When I finished spooning the first dozen of cookies, at the end of min6, my roommate can start his work. And when baking the second dozen, he can start cooling the first dozen and pack them. Assume we accept the payment after the cookies can be delivered, the total time of fill the order will be 36 min. Finally we accept the model and consider the situation of an x dozen(s) order, we can easily conclude that the total time is 16+10x minutes.
|Steps |Gantt chart of filling a order of 2 dozens of cookies(1min for 1 cell) |
|Wash&mix | |
Wash&mix | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |Spoon | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |Set oven | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |Bake | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |cool | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |Pack | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |...