Answer to Question #294350 in Accounting for Imran

Question

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:

Express revenue a a function of X:

Revenue function = P $\times$ Q

TR = P $\times$ Q

x = 60 – 3P

P = 20 – $\frac{x}{3}$

TR = (20 – $\frac{x}{3}$) $\times$ X = 20X – $\frac{X^{2}}{3}$

Total Revenue function = 20X – $\frac{X^{2}}{3}$

 

Expree profit as a function of x:

Profit = TR – TC

Profit = (20X – X²/3) – (72 + 6x)