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Slajd: 1
Nurse Chi, this new vaccine has really tight prep window. We need to be efficient. Let's say I can do 10 doses in 15 mins, you do 10 in 20 mins. Together for 50 doses? What do you think?
Okay, for those 5 minutes, our combined rate would be 2/3 + 1/2 = 7/6 doses per min. Time for 50 doses: 50/(7/6) = 43 minutes.
Slajd: 2
That's good to know! But what if you get pulled away for a few minutes, and your rate temporarily drops? Let's say for 5 mins, your rate goes down to 1/4 doses per minute. How would that affect our total time for those 50 doses?
So, we can get 50 doses ready in about 43 minuets working together.
Okay, so for 5 mins, our combined rate would be 2/3 + 1/4 = 8/12 + 3/12 = 11/12 doses per minute. Slower rate for 5 mins: 5 x (2/3+1/4) = 55/12 doses done. Remaining is 545/12 doses. Time at normal combined rate is 39 mins. Total time is 44 mins.
Slajd: 3
That's right! And what if we get a rush of patients, and we need to prepare at least 80 doses within an hour (60 mins)? What inequality could we see what our minimum combined rate needs to be?
So, a small slowdown does add a little bit of time.
We want the number of doses to be greater than or equal to 80 when the time is 60 minutes.

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