Average total cost question

Question

A company's average cost per unit when x units are produced is defined to be
Average cost = Total cost/x

Suppose a company's average costs are given by
Average cost = 8000/x + 35 + 0.7x.

 

(a) Express the average-cost formula as a single fraction.
Average cost =


(b) Write the expression that gives the company's total costs. (Simplify your answer completely.)

Answer 1

Average cost = 8000/x + 35 + 0.7x.

(a) Express the average-cost formula as a single fraction.  You need to put all three terms over a common denominator, in this case x:

Average cost = 8000/x + 35x/x + 0.7x²/x = (0.7x²+35x+8000)/x

(b) Write the expression that gives the company's total costs. (Simplify your answer completely.)

 

Average cost = Total cost/x,

so Total Cost = x*Average Cost

 

Total Cost = x*(0.7x²+35x+8000)/x = 0.7x² + 35x + 8000