In a metropolitan area, 45,000 people want to travel from the city suburbs to the city center. To do so, they can drive, take a city bus, or use the subway system. If x₁ number of people drive and x₂ number of people take a bus, it will take respectively 0.0006x₁+30 and 0.0003x₂+40 minutes to make the trip, whereas a subway trip is expected to take 45 minutes. The city bus system can transport a maximum of 20,000 people to the city center, while the subway system has a capacity of transporting at most 10,000. Write a programming formulation that minimizes the average travel time for each person.
