usage of "much"

Currently I'm reading "Essential Business Grammar and Usage" to give short lessons to my colleague who joined us about a year ago and is not confident in his English.
Reading Unit 3 from the "Verbs and tenses" section (there is/there are), I came across with this:

USES
2. Asking questions to find out something or someone exist
Are there many different production sites?
Is there a computer programmer here?
Is there much work to do?
Note: We use a lot of / plenty of in positive statements.
There is a lot of / plenty of work to do. (NOT*There is much work to do.)

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My question is about the last two sentences.
What exactly does "positive statements" mean here?
We should not use "much" in a sentence which is positive, i.e. not a question or negation?
Or does "much" have a negative connotation and should not be used in a positive sense, i.e. we can say "there is much work to do" but its meaning is different from "there is a lot/plenty of work to do"?

undrentide said:

What exactly does "positive statements" mean here?
We should not use "much" in a sentence which is positive, i.e. not a question or negation?
Or does "much" have a negative connotation and should not be used in a positive sense, i.e. we can say "there is much work to do" but its meaning is different from "there is a lot/plenty of work to do"?

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Yes, I assume "positive statements" just means cases that aren't negatives or questions:

Negative statement: "There isn't much work to do." This is fine.

Question: "Is there much work to do?" This is fine.

Positive statement: "There is much work to do". This is correct English and means exactly what you'd expect, but it is a formal written form and not very conversational. In conversational English one would say it another way, such as "There's a lot of work to do" or "There's plenty of work to do".

Thank you, eeky san, for your answer and explanation.
Now it is clear for me, especially this explanation of yours made everything very clear!

eeky said:

Positive statement: "There is much work to do". This is correct English and means exactly what you'd expect, but it is a formal written form and not very conversational. In conversational English one would say it another way, such as "There's a lot of work to do" or "There's plenty of work to do".

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May I ask you another question?
It's about contraction for "be verb".
I was taught at school that we can use the contracted form for be verb:
e.g. I am = I'm, she is = she's.
Almost all the reference materials on English grammar (in Japanese) shows the combination of pronoun + be verb but now I found this sentence in the book:

USES
2 Describing people
This is my boss. Her name's Brigitta and she's Swedish. She's 31 years old.

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I don't remember if I've ever seen 's as a contraction of is with a general noun.

Question: Besides pronouns, when it is possible to use contraction?

It is possible, and common in informal writing, to use 's as a contraction of "is" after almost any noun ("the man's walking towards us", "the road's closed", "the train's leaving now", etc. etc.) This reflects the usual conversational pronunciation in such situations, where one doesn't fully articulate the word "is" unless one is emphasising it.

There are a few cases, such as nouns whose singular ends in an "s" sound, where 's seems a bit awkward. For example, I would not write "the bass's too loud" {"bass" = bass guitar).

eeky san, thank you again!
Somehow I could not find this kind of information on the net, so your answer helps me a lot.
Thank you so much!