Answer to Question #297065 in Calculus for Ravi

Question

<e> Congratulations! You are hired in a business organization. In this company the market research department that you are the member recommended to manufacture and market a promising new product (x). After extensive surveys, the research department supported the recommendation with the demand function:

Dx = f (p) = 60 – 3 P

Where Dx is quantity demanded at price P during a month. Financial department has brought the cost function and is given by

C(x) = 72 + 6x

Now the team leader of the market research department ordered you to manipulate the following problems.

Express revenue as a function of X

Expresses profit as a function of X

Answer 1

Solution

Given the demand function is

$D(x)=f(P)=60-3P$

Here, $D$ is the quantity demanded at price $P$

And the cost function is

$C(x)=72+6x$

Now we know that Revenue is equal to the number of units sold times the price per unit

Therefore, the Revenue is

$R(x) = x\times P$

$R(x) = Px$ Revenue function in terms of "$x$"

Now, we know that Profit is calculated by subtracting the cost from the revenue collected. Therefore,

$Profit=R(x)-C(x)\\$

$Profit=Px - (72+6x)$

$Profit=(P-6)x -72$