Question

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Score: 0 of 1 pt 10 of 10 (10 complete) HW Score: 90%, 90 X 4.9.16 Question Help In a certain city, a car rental service has a fleet of about 7000 cars. The pattern of rental and return locations is given by the fractions in the table below Metro Airport Returned to Cars rented from City Airport Downtown 0.82 0.01 0.01 0.82 0.17 0.17 0.17 City Airport 0.01 Downtown 0.82 Metro Airport On a typical day, about how many cars will be rented or ready to rent from the downtown location? 388 . . V N More Enter your answer in the answer box and then click Check Answer All parts showing Clear All Check Answer o e é

Answer 1

solution cars=7000 Given city Airport 0.82 Downtown 0.01 0.82 metro Airport Returned to 0.17 7 city Airport 0.01 Downtown metro Airport Ta 0.01 0:17 0:17 The steady state vector will be [x y z ] Then XT=8 Steady state vector = [0-458 0.027 0.486] [These values are calculated and proot given below]. Number of cars will be rented from down town location = 0.027 X 7000 - 189 1189 cars aus Good luck

state vector proof coptional) steady XTOX 10.82 0:01 10.17 oool 082 0.17 0.17 7 ran 0.01 0.82 JL Hux x+y+z=1 0.827 +0.01 y 70-177 - - . 0.01X +0.824 +0.012-- 0.17 X +0.174 + 0-827-Z Now 070.01+0-172-X-0.82% cut o 17 z =x =) o-osyto.94 Z=0 0.18 - 0-0 (0-054 +0.942) +0.824 +0.012- y 0.017 +0.82y = y 0.01750:18 y 0.01 0.109+0:13 x+y+z =1 0.05+0-942+ y + z = 1 0.054 to.94x184+4 + 184 = 1 35.97 y 21 1 y=0.027 00012: 0:18 (0.027) Za0-486] 005 (0.027) +0.94 (o.ug 6 -X 10.458 => 1 Good luck.

i provided the calculation for steady state vector for understanding purpose and it is optional.

Thank you