Suppose people in a bank are waiting in two separate lines. Each minute several things happen: some

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Suppose people in a bank are waiting in two separate lines. Each minute several things happen: some people are served, some people join the lines, and some people switch lines. In particular, suppose that 1/10 of the people in the first line are served, and 3/10 of the people in the second line are served. Suppose the number of people who join each line is equal to 1/10 of the total number of people in both lines and that 1/10 of the people in each line switch to the other.
a. Suppose there are 100 people in each line at the beginning of a minute. Find how many people are in each line at the end of the minute.
b. Write a discrete-time dynamical system for the number of people in the first line, and another discrete-time dynamical system for the number of people in the second.
c. Write a discrete-time dynamical system for the fraction of people in the first line.
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