# What is the Optimal Production Level for Minimizing Average Cost per Unit?

• MHB
• karush
In summary, to minimize the average cost per unit in a factory with a total cost function of $C=0.5x^2+15x+5000$, where $x$ is the number of units produced, we first compute $\displaystyle \frac{C}{x}=0.5x+15+5000x^{-1}$ and then equate the derivative of this to zero. This leads to the answer of $x=100$ units.
karush
Gold Member
MHB
Average Cost. A manufacturer has determined that the total cost $C$ of operating a factory is
$C=0.5x^2+15x+5000$ where $x$ is the number of units produced.
At what level of production will the average cost per unit be minimized?
(The average cost per unit is $\frac{C}{x}$)

taking C' and setting to zero I got $-15$ but how is this going to give the ans which is
$x=100$ units.

thanks for help

Last edited:
You want to first compute:

$\displaystyle \frac{C}{x}=0.5x+15+5000x^{-1}$ where $\displaystyle 0<x$

Now, equate the derivative of this to zero.

MarkFL said:
You want to first compute:

$\displaystyle \frac{C}{x}=0.5x+15+5000x^{-1}$ where $\displaystyle 0<x$

Now, equate the derivative of this to zero.

$(\frac{C}{x})'=\frac{1}{2}-\frac{5000}{x^2}$

$(\frac{C'}{x})'=0$ then x=100$or$-100$so$100\$ is ans

r

## 1. What is the definition of "Average cost per unit"?

The average cost per unit is the total cost of producing or acquiring a certain number of units divided by the number of units. It is used to measure the average cost of producing each unit of a product or service.

## 2. How is "Average cost per unit" calculated?

The average cost per unit is calculated by dividing the total cost by the number of units. The formula is: Average Cost per Unit = Total Cost / Number of Units.

## 3. What is the importance of "Average cost per unit" in business?

"Average cost per unit" is important in business as it helps to determine the profitability of a product or service. By calculating the average cost per unit, businesses can make informed decisions about pricing, production, and cost management.

## 4. How does "Average cost per unit" differ from "Marginal cost"?

"Average cost per unit" and "marginal cost" are both measures of cost, but they differ in the way they are calculated. Average cost per unit takes into account the total cost of all units produced, while marginal cost only considers the cost of producing one additional unit.

## 5. How can a business reduce its "Average cost per unit"?

A business can reduce its average cost per unit by increasing efficiency in production, negotiating better deals with suppliers, and implementing cost-saving measures. It can also reduce costs by increasing the number of units produced or by diversifying its product or service offerings.

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