Case Report : Kristen’s Cookie Company (A1)
1. To know the time it will take us to fill a rush order, we have to know how many dozens the rush order requires. If it is only one dozen, we need 6 minutes for the washing and mixing steps, 2 minutes for the spooning, 10 minutes for the whole baking, 5 minutes to cooling down, 2 minutes for the packing and 1 minute for the payment. That is to say : 26 minutes. If we consider the order requires N dozens : we always need the first 8 minutes to do the washing and mixing steps and the spooning. As long as the oven can only contain 1 dozen, we need 10xN minutes for the baking of all of the N dozens. I can use the time my roomate needs to bake 1 dozen to produce new cookies (washing + mixing + spooning) if the next dozen order requires a different flavour or if I already made 3 dozens. Finally, my roomate can use the 9 minutes of each baking (except the first one) to do the cooling packing and payment of the previous dozen order. That is why, the time needed to fill a rush order of N dozens is : 8 + 10xN + 5 + 2 + 1 = 16 + 10xN minutes. 2. We assume we are open 4 hours each night. Using Question 1, we know we need 16 + 10xN minutes to fill a N dozens rush order. We want to maximize N knowing we have to have 16 + 10xN < 240. We easily find N = 22. We can fill 22 orders in a night. 3. For me : I only wash the mixer, mix ingredients and spoon the cookies that is why my valuable time for one order is 8 minutes. For my roomate : he sets the oven, remove cookies from it at the end of the baking, pack them and accept the payment that is why his valuable time for one order is : 1 + 0 + 2 + 1 = 4 minutes. 4. We know the costs of boxes and ingredients do not change so the only thing which can change is the cost of time. For 1 dozen, question 3 tells us we have a total valuable time of 12 minutes. For 2 dozens, we will have a total valuable time of 6 + 2 x (2 + 1 + 2) + 1= 17 minutes....
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