Question

If quantity demanded `Q=6000-3P`, where `P` is the price and total cost is given by `5000+2Q`, will the revenue be maximized at a price `202`?

Answer 1

There is something wrong with the question, but following should explain you how to approach the problem.

Explanation:

`Q=6000-30P` shows the shows the quantity demanded in the market at a price `P`. Observe that greater the price smaller the quantity demanded.

`TC = 5000+ 2Q`, shows the cost function of the commodity for the company. Observe that `5000` is fixed cost and `2` is the variable cost per unit.

If company manufactures the product exactly as demanded (i.e. no surplusses or shortages),

At a price of `202`, quantity demanded is `6000-30xx202=-60`, which cannot be supplied (it really means `60` units are purchased by the company from market) and hence, there appears to be something wrong with the question.

If price is `22`, quantity demanded would be `6000-30xx22=5340` and

revenue would be `22xx5340=117480`

and total cost to company would be `5000+2xx5340=15680` and hence a profit of `101800`.

Further toatl revenue when `Q` is demanded is `Pxx(6000-30P)=6000P-30P^2` and

total cost for company is `TC=5000+2(6000-30P)` or `17000-60P`.

Profit to company would be `6000P-30P^2-17000+60P`

or `-30P^2+6060P-17000`

and this will be maximised when `P=6060/(2xx30)=101`

which is `-30xx101^2+6060xx101-17000=584859`