Do you manufacture electricity and is electricity considered to be a
tangible product?

Answer depends on a classification one accepts.

According to common use

http://en.wikipedia.org/wiki/Product_(business)

electricity is a comodity.

It is not tangible. 

Tangible product has has physical extent. Contrast with Service.
http://www.ksl.stanford.edu/people/brauch/demo/product-theory/TANGIBLE-PRODUCT.html

By common meaning
tangible means
Discernible by the touch; palpable: a tangible roughness of the skin.
Possible to touch.
Possible to be treated as fact; real or concrete: tangible evidence.
Possible to understand or realize: the tangible benefits of the plan.
Law. That can be valued monetarily: tangible property.


http://www.answers.com/tangible&r=67

So -it is not tangible (Do no test this by tryng to touch it!)

and it is not manufactured (made by hand  (manualy) or made by humans)
http://www.answers.com/manufactured&r=67

If you want to be scientific (category you chose), people do not
buy electricity (electrons are around for free) but energy,
and to be really exact, they do nor buy just any energy, but energy they
can control and direct - one can say a prepared negative entropy.

 Negentropy is useful, but it is not a tangible product.

In my opinion yes and yes. I can't think of a simular commodity. One
unique thing about electricity is it must be used within mili-seconds
of the time it is manufactured.   Neil

I suppose it depends on what you mean by "manufacture". Certainly
electric *current* is made available on demand by a controlled
industrial process. But on the other hand, the electrically charged
particles, electrons, which are the conductors of current, aren't
manufactured by the electric power providers. The power company uses
electrons which have been present in the environment indefinitely
long.

That's not to say that human intervention cannot manufacture
electrons. In high energy laboratories quantities of electrons can be
produced, given that an equal number of anti-electrons are made
simultaneously. (The production of matched pairs of
particle/anti-particle in the lab is itself facilitated by electric
power, made available by commercial providers.) But the providers of
domestic power don't need to make new electric charge. They need only
to have some source of energy which can be used to do work on the
electronic charges in a wire.

"Do you manufacture electricity and is electricity considered to be a
tangible product?"

The common and more correct expression is to "generate" electricity: 
to bring into existance, cause to be; to produce by a chemical
process; to create by a vital or natural process  - to take some
definitions from the dictionary,
OR Google:  search with   define:generate

Now search with   define:manufacture
and you will find many examples, almost all of them resulting in a
product, something tangible:  you can touch it, take it with you if it
is not too big, it is an article, one of similar articles manufactured
in the same way.

For my thinking, electricity is not a tangible product, hence the use
of another verb to describe its production.