Optimization
The level of satisfaction an employe has on its job is determined by many factors. Obviously, the salary plays an important role, but also the fact that a work is "clean"(relaxed) or "dirty"(stressful) are also important. Suppose that for a specific employe the level of satisfaction can be expressed by the following utility function: u = √w − 2x, where w
is the wage per hour and the parameter x ∈ [0, 1] denotes the level of "pollutionöf the job: x = 0 corresponds to a "clean"job and x = 1 a "dirty"job. "Dirty"jobs are usually paid better than "clean"jobs. The relation between w and x is given by w = 2+6x.
a) Is this employe more happier in a complete "clean"job or a complete "dirty"job?
b) Determine the level of dirtiness x this employe likes most and determine the corresponding
wage.