Case report: Kristen's Cookie Company
Total= 26 minutes (6+2+1+1+2+5+9)
The time we need for the first dozen of cookies is 26 minutes (see question 1). But the next orders only take 10 minutes. We can explain that by the fact that first we are obliged to do the whole operation. Then the mixing(6min) and the dishing(2min) can be done will an other dozen is baking (10 minutes). In the same reasoning cooking, baking and paying can be done when another dozen of cookies is backing. So, for 4 hours (=240 minutes), we can write the following equation: 240 = 26 + 10*(x-1) where we can find x = 22,4 minutes as solution. That means that in 4 hours, it's possible to make 22,4 dozen of cookies. In other words, we can make 22 full orders in 4 hours. Question 3
The work I do is described in the picture of question 1 by the green part which represent 8 minutes (6 minutes for the mixing + 2 minutes for the dishing).
The red part is my roommate’s work which represent 4 minutes (1 minute to prepare the oven + 2 minutes for the packing + 1 minute to accept the payment)
To answer this question, we have to focus on valuable time. Moreover we see that the washing and the mixing take me the same time for one, two or three dozen of cookies. If we look at the table below, we can see that one dozen of cookies needs 12 minutes of human work, two dozen need 17 minutes and 3 dozen need 22 minutes.
To conclude, we can say that if we cook only one dozen of cookies, it will take 12 minutes of human work.
If we cook 2 dozen, it will take 8,5 minutes by dozen of human work (17 divided by 2). In this case we win 3,5 minutes by dozen.
If we cook 3 dozen, it will take 7,33 minutes by dozen of human work (22 divided by 3). In this case we win 4,67 minutes by dozen.
We can imagine that human work cost 30 euro/hour, so 0,5 euro/minute. For 2 dozen, we can make a maximum discount of 3,5 * 0,5=...
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