Question

PLEASE HELP I HAVE 10 MINUTES LEFT


A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equation C=0.04x2−5x+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?

Answer 1

Answer:

Manufacturers has to produce 63 DVD/Blu-Ray players to achieve a minimum cost of $644

Step-by-step explanation:

The cost equation is given as:

$C=0.04x^2-5x+800$

This is a quadratic equation in general form, which is:

$y=ax^2+bx+c$

Matching, we can say:

a = 0.04

b = -5

c = 800

The minimum occurs at  $x=-\frac{b}{2a}$

and the minimum value would be to place that "x" value into the equation.

First, we find the minimum using values of a and b:

$x=-\frac{b}{2a}=-\frac{-5}{2(0.04)}=\frac{5}{0.08}=62.5$

Plugging this into original, we get:

$C=0.04x^2-5x+800\\C=0.04(62.5)^2-5(62.5)+800\\C=643.75$

Rounding off to nearest whole number, we can say:

Manufacturers has to produce 63 DVD/Blu-Ray players to achieve a minimum cost of $644