Question

Company ABC 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 costs $23 to produce 2 widgets, $55 to produce 4 widgets, and $247 to produce 10 widgets. What is the total cost of producing 8 widgets?
A. $103
B. $153
C. $167
D. $177

Answer 1

The given function  is a quadratic equation. Any quadratic equation can be written in the form :

$C(x)=ax^{2}+bx+c$

The given points can be taken as (2,23) ,(4,55) and(10,247)

We form three equations with the given points

For point (2,23 ) the equation is

23   = 4a + 2b + c

For point (4,55) the equation is

55 = 16a + 4b + c

For point  (10,247) the equation is:

247 = 100a+10b+c.

Solving the three equations for a,b,c we have :

32 = 12a + 2b

  16 = 6a + b

and,

 192 = 84 a + 6b

 32 = 14a + b

Solving for a,b,c we have:

a=2  b=4   c=7

The quadratic equation is c(x)=$2x^{2}+4x+7.$

When x=8

c(x)=$2(8)^{2}+4(8)+7= 167.$]

Option C. $167 is the right answer.

Answer 2

The fit-table function seems to be 2 x^2+4 x+7.
So the correct option is C): "$167"