A national healthcare provider wants to establish clinics in a mediumsized city of 1,000,000 people. The area of the city is 1000 square miles. If the market penetration of the provider in the city is...

A national healthcare provider wants to establish clinics in a mediumsized city of 1,000,000 people. The area of the city is 1000 square miles. If the market penetration of the provider in the city is 20% of the population, the cost of a clinic is $250,000 per year, the cost per mile is $0.10, and each person is expected to make an average of four visits per year to the clinic(s),

(a) Find the optimal number of clinics for the provider to staff, using the model of Section 1.5.2.

(b) Compute the total cost of staffing this many clinics.

(c) Compute the average distance between a randomly selected patient and the nearest clinic.

(d) Note that the maximum distance (for the model of Section 1.5.2) is 1.5 times the average distance. Suppose the provider wants to ensure that no patient is more than 5 miles from the nearest clinic. How many clinics should the provider staff under these conditions? What is the new total cost of this configuration?

(e) Identify at least three problems associated with using the model of Section 1.5.2 in this context.