A bicycle rental company has three rental locations in FreshAire Park, denoted by A (the alpine trailhead), B (the botanical garden), and C (the castle). A customer may rent a bike from any of the three locations and return the bike to any of the three locations. The manager finds that customers return the bikes to to the various locations according to the following probabilities: Rented from
А B C
Returned to A .8 .3 .2
B .1 .2. .6
C .1 .5 .2
1) Solve the homogeneous system (I – P)q = 0. Remember that q is a probability vector, so its entries must sum to 1.
2) If the bike rental company has 1000 bikes at FreshAire Park, how many individual bike racks do they need at each of their locations?