Homework 7.7: Applications- Incl. Minimum and Maximum

Question

A certain electronics manufacturer found that the marginal cost C� to produce x DVD/Blu-ray players can be found using the equation C=0.03x²−8x+800.If the marginal cost were $1831, how many DVD/Blu-ray players were produced?

___________

Answer 1

0.03x² - 8x + 800 = 1831; 0.03x² - 8x - 1031 = 0; 3x² - 800x - 103100 = 0; x = (400 ± √160000 + 309300)/3 =

362

Answer 2

So, you would solve for x as follows, where the format is 0=ax²-bx+c so that

1831 - 1831 = 0.03x²-8x+800 -1831

0 = 0.03x²-8x+(-1031)

_______

-b +/- _/ b²-4ac

x= ---------------------- (quadratic equation)

2a

_________________

-(-8) +/- _/ (-8)²-4(0.03)(-1031)

x= ------------------------------------------

2(0.03)

____________

8 +/- _/ 64 + 123.72

x= ------------------------------------

0.06

8 +/- 13.70

--------------- and this would have to be a positive number, so use 8+13.7=21.7

0.06

x= 361 DVD/Blu-ray players produced (rounding down)