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