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

$C=0.03x^2-7x+800$

The Average Cost function is defined as

$\displaystyle\bar C=\frac{C}{x}$

$\displaystyle\bar C=\frac{0.03x^2-7x+800}{x}$

$\displaystyle\bar C=0.03x-7+\frac{800}{x}$

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

$\displaystyle\bar C'=0.03-\frac{800}{x^2}$

Equating to 0

$\displaystyle 0.03-\frac{800}{x^2}=0$

Solving for x

$\displaystyle x=\sqrt{\frac{800}{0.03}}$

$x=163$

The second derivative is

$\displaystyle\bar C''=\frac{1600}{x^3}$

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

$\displaystyle\bar C(163)=0.03\cdot 163-7+\frac{800}{163}$

$\displaystyle\bar C(163)=2.80$

The minimum average cost is $2.80

5 0

3 years ago

Brums [2.3K]

Answer:

The answer is 3+(-6) = -9, because -9 is 6 units to the left of 3.

5 0

2 years ago

Read 2 more answers

If the ratio of surface areas of 2 similar figures is 144/25 ; What is the ratio of their volumes?

kkurt [141]

Answer:

1728/ 125

Step-by-step explanation:

The ratio of corresponding lengths of the figures = ratio of the square root of their areas.

So ratio of lengths = 12/5.

Now volume is 3 dimensional so the ratio is the cube of the lengths

= 12^3/5^3

= 1728/ 125.

7 0

3 years ago