photo necessities produces camera cases. they have found that the cost, c (x), of making x camera cases is a quadratic function in terms of x.

the company also discovered that it cost $28 to produce 2 camera cases, $50 to produce 4 camera cases, and $140 to produce 10 camera cases.

Find the total cost of producing 12 camera cases??????

Question

photo necessities produces camera cases. they have found that the cost, c (x), of making x camera cases is a quadratic function in terms of x.  

the company also discovered that it cost $28 to produce 2 camera cases, $50 to produce 4 camera cases, and $140 to produce 10 camera cases.

Find the total cost of producing 12 camera cases??????

anonymous · Answer

@micahm

micahm · Answer

name of lesson

anonymous · Answer

soving prblems with quadratic functions

micahm · Answer

i am not good with theis problem but i know who is @mathmath333  they might help 
sorry

anonymous · Answer

need help @mathmath333

anonymous · Answer

you got anything @mathmath333

mathmath333 · Answer

ya wait

mathmath333 · Answer

$\tt \color{black}{\text{since c(x) is quadratic function,thus }}$

$\large\tt \color{black}{c(x)=mx^2+nx+p}$

$\tt \color{black}{\text{and }}$

$\large\tt \color{black}{c(2)=mx^2+nx+p}$

$\large\tt \color{black}{28=m(2)^2+n(2)+p}$

$\large\tt \color{red}{m4+n2+p=28--A}$

$\tt \color{black}{\text{similarly}}$

$\large\tt \color{black}{c(4)=m(4)^2+n(4)+p}$

$\large\tt \color{red}{m16+n4+p=50--B}$

$\large\tt \color{black}{c(10)=m(10)^2+n(10)+p}$

$\large\tt \color{red}{m100+n10+p=140--C}$


$\tt \color{black}{\text{solve A B and C ,system of linear equations}}$

anonymous · Answer

i dont understand
@mathmath333

mathmath333 · Answer

first read it carefully 
what i have done
the three equations which are in red line , u have to solve them ,

anonymous · Answer

yeah but how do i solve them 
@mathmath333

mathmath333 · Answer

u can do matrix method,or by substitution method or any other

anonymous · Answer

i dont get this at all

mathmath333 · Answer

once u find m ,n and p 

u have to find 


$\large\tt \color{black}{c(12)=m(12)^2+n(12)+p}$

mathmath333 · Answer

c(12) will be the cost of 12 cameras

anonymous · Answer

what is c though?

anonymous · Answer

@mathmath333

mathmath333 · Answer

u mean answer

mathmath333 · Answer

well method here seems to be tough here 

there can be simpler methods but i dont know

anonymous · Answer

i dont know how ot do it ill just get it wrong i guess cause idk

anonymous · Answer

@mathmath333

mathmath333 · Answer

well i found one simpler method on a site

All quadratic equations are of the form: y = ax² + bx + c 
You need to find a,b,c given values for y and x 

y = 28 = a(2)² + b(2) + c 
y = 50 = a(4)² + b(4) + c 
y = 140 = a(10)² + b(10) + c 

... simplify ... 

28 = 4a + 2b + c (i) 
50 = 16a + 4b + c (ii) 
140 = 100a + 10b + c (iii) 

... now you have three simultaneous equations. Solve as normal. 

(ii) - (i): 
22 = 12a + 2b 
... 11 = 6a + b 
... b = 11 - 6a 

(iii) - (ii): 
90 = 84a + 6b 
... 15 = 14a + b 
... b = 15 - 14a 

15 - 14a = 11 - 6a 
15 - 11 = -6a + 14a 
4 = 8a 
a = ½ 

b = 11 - 6a = 11 - 6(½) = 11 - 3 = 8 

28 = 4a + 2b + c 
c = 28 - 4a - 2b = 28 - 4(½) - 2(8) = 28 - 2 - 16 = 10 

So your cost function c(x) is ½x² + 8x + 10

mathmath333 · Answer

$\large\tt \color{black}{c(12)=\frac{x^2}{2}+8x+10}$

$\large\tt \color{black}{c(12)=\frac{{12}^2}{2}+8\times 12+10}$

$\large\tt \color{black}{c(12)=\frac{144}{2}+96+10}$


$\large\tt \color{black}{c(12)=72+96+10}$


$\Huge \tt \color{black}{c(12)=176}$

anonymous · Answer

i still dont understand but you tryed i gave you a medal @mathmath333

mathmath333 · Answer

http://www.purplemath.com/modules/systlin1.htm http://www.mathsisfun.com/algebra/systems-linear-equations.html