Mathematics

Problem

A manufacturer models the production of

x

units (

x>0

) with the following functions: Variable cost per batch:

v(x)=\sqrt{5x+20}

, Fixed cost:

c(x)=1000

(in rupees), Selling price per unit:

r(x)=50-\dfrac{1}{x-2}

. a. (i) Write the total revenue function

R(x)

and the total cost function

C(x)

. b. (ii) Derive the average profit per unit

A(x)=\dfrac{R(x)-C(x)}{x}

and simplify it. c. (iii) Determine the domain of

A(x)

and interpret the practical meaning of any restrictions obtained.