$1.$ This first problem compares the point$-$to$-$point route structure operated by the archetypal low$-$cost carrier $($LCC$)$ with the hub$-$and$-$spoke network route system typical of a full$-$service network carrier $($FSNC$).$ Recall that the pure point$-$to$-$point system does not offer passenger connections to other cities.$$ The network carrier, on the other hand, offers many connections at its hub to the spoke cities in its network.$$ For the problems, assume the LCC operates a point$-$to$-$point route system and the FSNC operates a hub$-$and$-$spoke system.$$ Also, assume both airlines operate aircraft configured at $180$ seats.$$ A city$-$pair is City A to City B$.$ A to B and B to A are considered just one city$-$pair $($a two$-$way network$).$

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a$.$ If the LCC is operating a $180-$seat aircraft in city pair A$-$B$,$ how many passengers from city A must be bound for city B to achieve an $80\%$ load factor $($don$$t overthink this, it$$s easy!$)?$

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b$.$ The FSNC operates a single hub that connects $44$ spoke cities $($or nodes in network terminology$).$ How many city pairs does it serve?$$ Recall that the hub is a major destination for the FSNC$.$

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c$.$ The FSNC adds a $45$th spoke city to its network.$$ On a flight from this new $45$th spoke to the hub, how many passengers, on average, does it need to attract to each destination, including the hub, to achieve an $80\%$ load factor?$$ Hint: the number of passengers on this flight cannot be more than the seating capacity.$$

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d$.$ How can the FSNC profitably serve smaller cities that the LCC cannot? $($Hint:$$ Consider $1$c above$).$

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e$.$ A regional partner airline under contract to the FSNC serves some small cities close to the FSNC$$s hub with regional jets that have much higher seat$-$mile$-$costs $($CASM$)$ than larger mainline jets.$$ The average fare from these cities to the hub does not cover the fully allocated cost.$$ Is this economically rational?$$

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f$.$ Networks are subject to negative network externalities.$$ How might such externalities affect the FSNC$$s decision to add another spoke city to its network?$$ Explain.

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