Question

PLEASE HELP.

Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.



The company also discovered that it cost $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.


Find the total cost of producing 6 widgets.

Answer 1

quadratic
y = ax^2 + bx + d
c (x) = ax^2 + bx + d
c (3) = a (3^2) + b (3) + d
c (3) = 9a + 3b + d = 15.50

c (7) = a (7^2 + b (7) + d

c (7) = 49a + 7b + d = 23.50

c (12) = a (12^2) + b (12) + d
c (12) = 144a + 12b + d = 56

solve using simultaneous equations... to get a b and d

use that to solve for x = 5

hope this helps?

Answer 2

The total cost of producing 6 widgets is $231.

Explanation:

Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.

To find : The total cost of producing 6 widgets.

Solution :

Cost is given by
`c (x) = ax^2 + bx + d`

• Cost $23 to produce 2 widgets,

`c(2) = a(2)^2 + b(2) + d`

`23= 4a+2b+d` .........[1]

• Cost $103 to produce 4 widgets,

`c(4) = a(4)^2 + b(4) + d`

`103= 16a+4b+d` ............[2]

• Cost $631 to produce 10 widgets.,

`c(10) = a(10)^2 + b(10) + d`

`631= 100a+10b+d` ...........[3]

Now, we solve equation [1], [2] and [3]

Subtract equation [2]-[1] and [3]-[2]

[2]-[1] →
`12a+2b=80` ........[4]

[3]-[2] →
`84a+6b=528` .......[5]

Solving equation [4] and [5] by elimination method,

Multiply equation [4] by 3 and subtract from [5]

`84a+6b-3(12a+2b)=528-3(80)`

`84a+6b-36a-6b=528-240`

`48a=288`

`a=6`

Put in equation [4]

`12(6)+2b=80`

`72+2b=80`

`2b=8`

`b=4`

Substitute the value of a and b in [1] to get d

`23= 4a+2b+d`

`23= 4(6)+2(4)+d`

`23= 24+8+d`

`23= 32+d`

`d=-9`

Substitute a=6,b=4,d=-9 in the cost equation,

The required equation form is
`c(x) = 6x^2 + 4x-9`

The total cost of producing 6 widgets.

Put x=6

`c(6) = 6(6)^2 + 4(6)-9`

`c(6) = 216+15`

`c(6) =231`

Therefore, The total cost of producing 6 widgets is $231.