Consider a corporation with a factory producing pollution that decays with distance (d) in kilometers at a rate: P = 1 / d^2.

Workers must live some distance (d) away from the factory in order to work there and suffer health costs equal to $1/unit of pollution they are exposed to at home. The cost of commuting is $1 per kilometer of distance. Workers cannot live closer than 0.1km away from the factory.

1. Describe the tradeoff workers must make in deciding where to live, and write an expression for workers' total cost function (including both health and transportation costs).

2. How close to the factory will a representative worker decide to live, assuming that they are a cost minimizer? [reminder: 1/x^2 = x^-2, and the derivative of x^n is nx^(n-1)]

3. Suppose the factory perfectly compensates workers for health damages due to pollution, wherever they live. How close to the factory will workers choose to live?