The Sayre-Priors Airline operates the following set of scheduled flights: Flight No. 101 410 220 17 7 13 11 19 23 3 Origin Chicago New York New York Miami LA Chicago Miami Chicago LA Miami Tour 17, 101, 23 220, 17, 101 410, 13 Cost Destination Time of Day LA Chicago Miami $2,000 $3,000 $2,000 Chicago Chicago New York: New York One-flight tours (All Miami Miami LA The Flight Operations Staff would like to set up a low cost crew assignment schedule. The basic problem is to determine the next flight, if any, that a crew operates after it completes one flight. A basic concept needed in understanding this problem is that of a tour. The characteristics of a tour are as follows: afternoon afternoon - A tour consists of from 1 to 3 connecting flights. - A tour has a cost of $2,000 if it termintates in its city of origin. - A tour which requires "deadheading", i.e., terminates in a city other than the origin city, costs $3,000. In airline parlance, a tour is frequently called a "pairing" or a "rotation". The following are examples of acceptable tours: night morning afternoon night morning night night afternoon The first thing to do for this small problem is to enumerate all feasible tours. We do not consider a collection of flights which Involve an intermediate layover a tour. There are 10 one-flight tours, and either 37 or 41 three flight tours depending upon whether on distinguishes the origin city on a nondead-heaing tour. These tours are indicated below: + - B 4 5 The first thing to do for this small problem is to enumerate all feasible tours. We do not consider a collection of flights which involve an intermediate layover a tour. There are 10 one-flight tours, and either 37 or 41 three flight tours depending upon whether on distinguishes the origin city on a nondead-heaing tour. These tours are indicated below: One-flight tours (All costs $3,000) 1 2 3 4 5 6 7 8 9 10 101 410 220 17 7 13 11 19 23 3 Two-flight tours 11 12 13 14 15 16 17 2222222 18 19 20 21 23 24 101, 23 410, 13 410, 19 220, 17 220, 11 17,101 7,13 7,19 11, 410 19, 17 19, 11 23, 17 23, 11 3,23 $ $ $ $ sss $ $ $ ss $ $ nn $ $ ssss $ $ Cost 3,000 2,000 3,000 3,000 2,000 3,000 3,000 3,000 3,000 2,000 3,000 3,000 3,000 2,000 Three-flight tours 25 26 27 28 29 30 25 31 32 33 28 34 28 25 35 36 37 101, 23, 17 101, 23, 11 410, 19, 17 410, 19, 11 220, 17, 101 220, 11,410 17, 101, 23 7,19, 17 7, 19, 11 11,417, 13 11, 410, 19 19, 17, 101 19, 11, 410 23, 17, 101 23, 11, 410 3,23, 17 3, 23, 11 Cost $ 2,000 $ 3,000 $ 3,000 $ 2,000 $3,000 $3,000 $ 2,000 $ 3,000 $ 3,000 $ 3,000 $ 2,000 $3,000 $ 2,000 $ 2,000 $ 3,000 $ 3,000 $ 3,000 Formulate the problem to find the minimum cost of scheduling the crews to make sure every flight will be able to depart at the time scheduled. Hint: We do not distinguish the city of origin on nondeadheading three flight tours. That's why the tour with flights 101, 23, 17 is the same as 17, 101, 23. + M