Title: Simultaneous Optimization

References:

http://pollux.usc.edu/~agoel/papers/majorize_practical.ps
and
http://pollux.usc.edu/~agoel/papers/aggregate.ps

Three questions (Pick one and answer it as a one-page essay, please provide brief and to the point answers):

a) Find two real life examples that demonstrate economies of scale, and two real life examples that
demonstrate diminishing returns. A real life example could be something like a price quote from a web page.

b) Use Jensen's inequality to establish an inequality between E[2^X] and 2^[E[X]] where X is an arbitrary random variable, and E denotes expectation.

c) Find two real life examples where simultaneous optimization is important.

Lecture notes: Here