# The cost per day of running a hospital is 200,000 + .002x 2 dollars, where x = patients served per..

The cost per day of running a hospital is 200,000 + .002×2 dollars, where x = patients served per day. What size hospital minimizes the per-patient cost of running the hospital? Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the subway, the trip lasts 40 minutes. If x thousand people per morning drive to New York, it takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact of life: If people are left to their own devices, they will cause more congestion than need actually occur! a. Show that if people
The cost per day of running a hospital is 200,000 + .002×2 dollars, where x = patients served per day. What size hospital minimizes the per-patient cost of running the hospital? Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the subway, the trip lasts 40 minutes. If x thousand people per morning drive to New York, it takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact of life: If people are left to their own devices, they will cause more congestion than need actually occur! a. Show that if people are left to their own devices, an average of 4,000 people will travel by road from New Jersey to New York. Here you should assume that people will divide up between the subways and roads in a way that makes the average travel time by road = aver-age travel time by subway. When this equilibrium occurs, nobody has an incentive to switch from road to subway or subway to road. b. Show that the average travel time per person is minimized if 2,000 people travel by road.

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