Question

A certain electronics manufacturer found that the average cost C C to produce x DVD/Blu- ray players can be found using the equation C = 0.03 x 2 − 5 x + 700 C=0.03x2-5x+700. What is the minimum average cost per machine and how many DVD/Blu-ray players should be built in order to acheive that minimum?

Answer 1

Answer:

83,491.67 dollars

Step-by-step explanation:

Given that a certain electronics manufacturer ound that the average cost C C to produce x DVD/Blu- ray players can be found using the equation  $C=0.03x^2-5x+700$

To find the minimum average cost per machine we can use derivative test.

we find first and second derivative.

If for a particular value of x first derivative is 0 and second derivative is positive, then that x satisfies the minimum cost criteria.

$C=0.03x^2-5x+700\\C'(x) = 0.06x-5\\C"(x) = 0.06>0$

Second derivative is always positive

I derivative =0 gives

$x=5/0.06 \\=83.33\\~83$

For 83 players the cost would be minimum

Minimum cost = $0.03(83)^2-5(83)+700\\=491.67$