Question

The company discovered that it costs $45 to produce 4 camera cases, $257 to produce 7 camera cases, and $792 to produce 12 camera cases. Using quadratic function, find the cost of producing 1 camera case.

Answer 1

How we play in the matrix..... its the same as the other one I just did but without the letters cluttering it up

Answer 2

(4,45) (7,257) (12,792)

16x^2 +4x +c = 45
49x^2 +7x +c = 257
144x^2 +12x +c= 792

| 16 4 1 || 45 |
| 49 7 1 || 257 |
|144 12 1 || 792 |

is the setup

Answer 3

| 16 4 1 || 45 | (1/16)

| 1 1/4 1/16 || 45/16 |
| 49 7 1 || 257 |
|144 12 1 || 792 |

| 1 1/4 1/16 || 45/16 | (-49)
| 49 7 1 || 257 |

|-49 -49/4 -49/16 || -2205/16 |
| 49 28/4 16/16 || 4112/16 |
-------------------------------
| 0 -21/4 -33/16 || 1907/16 |
-------------------------------

| 1 1/4 1/16 || 45/16 | (-144)
|144 12 1 || 792 |

|-144 -144/4 -144/16 || -6480/16 |
|144 48/4 16/16 || 12672/16 |
----------------------------------
| 0 -96/4 -128/16 || 6192/16 |
----------------------------------

Answer 4

| -21/4 -33/16 || 1907/16 | (-4/21)
| -96/4 -128/16 || 6192/16 |

| 1 33/84 || -1907/84 | (96/4)
| -96/4 -128/16 || 6192/16 |

| 96/4 66/7 || -3814/7 |
| -96/4 -56/7 || 2709/7 |
-------------------------
| 0 10/7 || -1105/7 |
-------------------------

| 10/7 || -1105/7 | (7/10)

| 1 || -221/2 |

c = 110.5

Answer 5

c = -110.5 lol

Answer 6

| -21/4 -33/16 || 1907/16 |
| 0 1 || -1105/10 | (33/16)

| -21/4 -33/16 || 3814/32 |
| 0 33/16 || -7293/32 |
---------------------------
| -21/4 0 || -3479/32 | (-4/21)


| 1 0 || 3479/168 |

b = 3479/168
c = -1105/10

its quicker on paper, and less mistakes...

ill do it up and give you and answer ;)

Answer 7

1 case costs $18.67 cents; if I did it right... and I have my doubts with it cause of all the fractions, but thats my best guess :)

Answer 8

my computer just froze & shut everything down -_-

Answer 9

Another approach to this problem is to use a curve fitting program.
The general form of a quadratic equation is: y(x) = a*x^2 + b*x + c.
Given a set of data, the curve fitting program will calculate the optimum values for the constants a, b and c using a "least squares" method. Refer to: http://mathworld.wolfram.com/LeastSquaresFitting.html

Let y(x) be equal to the cost to produce a batch of x camera cases.
From three direct measurements the company had determined that the cost to produce a batch of 4, 7 and 12 camera cases was 45, 257 and 792 dollars respectively. The company wants to know the approximate cost to produce 1 case based on their past production experience.

The following Mathematica 8 statement will compute the values for a, b and c for this problem.

Fit[{{4, 45}, {7, 257}, {12, 792}}, {1, x, x^2}, x]
If the reader has no access to Mathematica 8, then copy and past the above into the "=" input box at
www.WolframAlpha.com

Answer 10

The result is 4.54167 x^2 + 20.7083 x -110.5 and evaluated at x=1 is -85.25

If the numbers above are rationalized,that is, made into fractions, the f[x] can be written as:
\[ \frac{109}{24}x{}^{\wedge}2+\frac{497}{24}x-\frac{221}{2} \]
Refer to the attachment, CameraCase.pdf, which is a plot of f(x).
The plot shows that any batch less than 4 is a looser.