Solve application problems using quadratic functions.

Question

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 - 6x + 700. What is the minimum average cost per machine and how many DVD/Blu-ray players should be built in order to achieve that minimum?

Answer 1

There are several ways on how to solve this problems but let me solve it to you in a simple way. The function:

C(x) = 0.03x² - 6x + 700 is quadratic in standard form:

C(x) = ax² - bx + c. Because a > 0, the graph of this equation is parabola open up. Therefore it has a minimum. The coordinates of the minimum are

( -b , C(-b ) )

2a 2a

Therefore we can say:

-b => is the number of DVD/Blu-ray players should be built in order to achieve that minimum

2a

C(-b/(2a) ) = is the minimum average cost per machine.

-b = -(-6) = 100

2a 2(.03)

C(100) = 0.03(100)² - 6(100) +700 = 400 units of DVD/Blu-ray

Note: 100 is probably in dollars but monetary unit is never mentioned in the problem. Tell your teacher to be very specific next time.