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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

Verified Answer :

syed514

The fit-table function seems to be 2 x^2+4 x+7.

So the correct option is C): "$167"

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.



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