Question

The total cost of producing x units of a product is estimated by the cost function

C = f(x) = 60x + 0.2x² + 25,000

where C equals total cost measured in dollars.  

a) This function is an example of what class of functions?

b) What is the cost associated with producing 25,000 units?

c) What is the cost associated with producing zero units? What term might be used to describe this cost?

Answer 1

C = f(x) = 60x + 0.2x² + 25,000
a) This function is an example of what class of functions?
Ans: The given cost function C belongs to the quadration equations class of functions and graph can be represented by a parabola.

b) What is the cost associated with producing 25,000 units?
Ans: For knowing the cost of such a scenario, put x=25000 in the cost function equation
C = f(x) = 60x + 0.2x² + 25,000 = 60*25000 + 0.2 * (25000)² + 25000 = 12,65,25,000

c) What is the cost associated with producing zero units? What term might be used to describe this cost?
Ans: For this scenario, put x = 0. Hence we get the cost as 25000. This cost, which is independent of the number of units produced, is called as fixed cost.