The supervisor of an assembly line has two tool cabinets, one at each end of the assembly line. Every morning, she walks from one end of the line to the other, and she is equally likely to begin the walk at either end. In the two tool cabinets are a total of six flashlights. At the beginning of her walk, the supervisor takes a flashlight (if one is available) from the tool cabinet at the location, and at the end of her walk, she leaves a flashlight (if she possesses one) at the tool cabinet at that location. Model the movement of flashlights using a discrete-time Markov chain. (Hint: track the number of flashlights at either end of the assembly line.)
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