Citylove airlines runs daily flights operating to and frobetween Chicago (ORD) and each of the three cities of San Francisco(SFO), Boston (BOS), and New York (JFK) The network is shown inthe figure below Seats on any of these journeys are available forindividual purchase Additionally, one can also buy tickets for theSFO to JFK via ORD itinerary and the SFO to BOS via ORD itineraryfor a reduced price as compared to purchasing the individualjourneys separately The list of products that the airline offersfor purchase and the associated fares are presented in the tablebelow Consider selling tickets over a booking window of 101 timeperiods, with initial capacity of 50 seats on all flights In eachperiod, the airline gets at most one request for a particularproduct, where product j is requested with probability j The per period request probabilities forthe products are also presented in the table Answer the questionsbelow Product Total Fare Per period arrivalprobability SFO ORD 150 0 15 JFK ORD 75 0 1 BOS ORD 80 0 1 ORD SFO 180 0 1 ORD JFK 85 0 15 ORD BOS 90 0 1 SFO ORD JFK 200 0 1 SFO ORD BOS 225 0 1 (1 point) Let m denote the number of resources and n denote the number of products being managed daily by theairline What is m and n Suppose that you are in time period t 1 and you have50 seats left on all flights Write down the deterministic linearprogramming formulation that computes the approximation V F luid ( 50 , 50 , 50 , 50 , 50 , 50 ) to the valuefunction Write down a linear program that computes the shadow prices forseats on each of the flight legs and for unit demands for each ofthe different products when t 1 and you have 50 seatsleft on all flights Assume that you are using the deterministiclinear programming formulation Suppose that the shadow prices for a seat on the SFO ORD flightis $130 and a seat on the ORD JFK flight is $75 Based on thebid price control mechanism, will you accept a SFO to JFK via ORDrequest

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Citylove airlines runs daily flights operating to and frobetween Chicago (ORD) and each of the three cities of San Francisco(SFO), Boston (BOS), and New York (JFK). The network is shown inthe figure below. Seats on any of these journeys are available forindividual purchase. Additionally, one can also buy tickets for theSFO to JFK via ORD itinerary and the SFO to BOS via ORD itineraryfor a reduced price as compared to purchasing the individualjourneys separately. The list of products that the airline offersfor purchase and the associated fares are presented in the tablebelow. Consider selling tickets over a booking window of 101 timeperiods, with initial capacity of 50 seats on all flights. In eachperiod, the airline gets at most one request for a particularproduct, where product j is requested with probability?_j. The per-period request probabilities forthe products are also presented in the table. Answer the questionsbelow

Product	Total Fare	Per-period arrivalprobability
SFO-ORD	150	0.15
JFK-ORD	75	0.1
BOS-ORD	80	0.1
ORD-SFO	180	0.1
ORD-JFK	85	0.15
ORD-BOS	90	0.1
SFO-ORD-JFK	200	0.1
SFO-ORD-BOS	225	0.1

1. (1 point) Let m denote the number of resources andn denote the number of products being managed daily by theairline. What is m and n?
1. Suppose that you are in time period t = 1 and you have50 seats left on all flights. Write down the deterministic linearprogramming formulation that computes the approximation V^F^luid([50, 50,50, 50, 50, 50]) to the valuefunction
2. Write down a linear program that computes the shadow prices forseats on each of the flight legs and for unit demands for each ofthe different products when t = 1 and you have 50 seatsleft on all flights. Assume that you are using the deterministiclinear programming formulation
3. Suppose that the shadow prices for a seat on the SFO-ORD flightis $130 and a seat on the ORD-JFK flight is $75. Based on thebid-price control mechanism, will you accept a SFO to JFK via ORDrequest?