2. You're in charge of logistics for a nearby supermarket! You want to model how your supply of pasta will vary depending on the behaviour of your shoppers. To do this, you've created the following model for your supply of pasta Pn over time: Pn+1 = max ( Pn + min(300, 600 - PR) - (200 + 50 . f(Pn)), 0 ) where f : Z -> Z is the piecewise-defined function f(n) = ] 3 50 > n. on f (m )- 1, n 2 50, The terms here are justified as follows: on day n + 1, your supply of pasta Pati is . the pasta you have left over from yesterday (PR), . plus the new pasta shipped in (either 300, the maximum # of pasta boxes your distributor can send, or 600 - Pn, the maximum pasta you can stock on your shelf/ warehouse), . minus the pasta you sold. There are two kinds of customers that buy your pasta: - Stable customers. They buy 1 box of pasta per trip, and there are 200 of them daily.- Panicky customers. If, on their last trip to the shops, it looked like there was a lot of pasta (i.c. Pn 2 50), they shop normally and buy a box of pasta. However, if they heard from their friends that pasta is running low, (i.c. Pn