Question

PLEASE HELPPPPPP

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 $45 to produce 3 camera cases $257 to produce 7 camera cases and $792 to produce 12 camera cases.


Find the total cost producing 1 camera case

Answer 1

The total cost producing 1 camera case is:

$ 11

Explanation:

Let the quadratic function be:

`c(x)=ax^2+bx+c`

Now, c(3)=45

This means:

`9a+3b+c=45------------(1)`

c(7)=257

This means that:

`49a+7b+c=257----------------(2)`

and c(12)=792

This imply:

`144a+12b+c=792-------------------(3)`

On subtracting first equation from second we get:

`40a+4b=212------------(4)`

and on subtracting second equation from third we get:

`95a+5b=535-----------(5)`

Now on multiplying equation (4) by 5 and equation (5) by 4 and subtracting both equation we get:

a=6

Putting value of a in equation (4) we get:

b= -7

and putting the value of a and b in equation (1) we get:

c=12

Hence, the cost function is:

`c(x)=6x^2-7x+12`

Now, the cost of producing 1 camera will be the value of c(x) when x=1

i.e.

`c(1)=6-7+12\\\\\\c(1)=11`

Hence, the answer is:

$ 11

Answer 2

The first thing you should know is that to define a quadratic function you need three points.
In this case the points will be:
(3. 4. 5)
(7, 257)
(12, 792)
The equation of the quadratic function in this case will be:
c (x) = 6x ^ 2 - 7x + 12
Therefore for x = 1 we have:
c (1) = 6 * (1) ^ 2 - 7 * (1) + 12
c (1) = 11 $
Answer:
Total cost producing 1 camera case is:
c (1) = 11 $