A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equation C=0.03x2−7x+800. What is the minimum average cost per machine and how many DVD/Blu-ray players should be built in order to acheive that minimum?

The minimum average cost is $2.80 when 163 players are built

Step-by-step explanation:

Average Cost Function

We'll assume the given function as the total cost to produce x players, and NOT the average cost since that is a different definition, as shown below.

The cost C to produce x DVD/Blu- ray players is given by the equation

The Average Cost function  is defined as

To find the extreme value of the average cost, we must take the first derivative of the function

Equating to 0

Solving for x

The second derivative is

For x=163 the second derivative is positive, thus x=163 is a minimum value. Let's compute the minimum average cost

The minimum average cost is $2.80

step-by-step explanation:

where is the questions