Question

Average Cost Suppose that the daily cost Cof manufacturing bicycles is given by $C\left(x\right)=80x+5000$. Then the average daily cost $\overline{C}$is given by $\overline{C}\left(x\right)=\frac{80x+5000}{x}$. How many bicycles must be produced each day for the average daily cost to be no more than $ 100?

Short answer

At least 250 objects must be produced each day.

Step-by-step solution

Given information

The average expenses for a day are given by:

$\overline{C}\left(x\right)=\frac{80x+5000}{x}$

Determine the number of bicycles must be produced each day for the average daily cost to be no more than $ 100.

Write the inequality so that the average expenses are less than or equal to $ 100:

$\begin{array}{rcl}C\left(x\right)& \le & 100\\ \frac{80x+5000}{x}& \le & 100\\ 80x+5000& \le & 100x\\ 5000& \le & 20x\\ x& \ge & 250\end{array}$

Write the conclusion

At least 250 bicycles must be produced each day for the average daily cost to be no more than $ 100.