$2.$ Airlines often provide both passenger and cargo services. Analyze whether economies of scope exist in this dual$-$service model by considering the following scenario: Airline X operates both passenger and cargo services. Passenger service involves transporting passengers between cities, while cargo service involves transporting goods and packages. Airline X has fixed costs associated with maintaining its fleet, airport facilities, and administrative expenses. Additionally, it incurs variable costs per passenger and per unit of cargo transported. Suppose Airline X has the following cost structure for a given period:

Fixed costs $($F$)=$ $$5,000,000$

Variable costs per passenger $($VCp$)=$ $$100$

Variable costs per unit of cargo $($VCc$)=$ $$50$

Total passenger demand $($Qp$)=50,000$ passengers

Total cargo demand $($Qc$)=5,000$ units

a$)$ Calculate the total cost $($TC$)$ for Airline X when it operates only passenger service.

b$)$ Calculate the total cost $($TC$)$ for Airline X when it operates only cargo service.

c$)$ Calculate the total cost $($TC$)$ for Airline X when it operates both passenger and cargo services simultaneously.

d$)$ Determine whether economies of scope exist for Airline X based on your calculations in parts $($a$),($b$),$ and $($c$).$