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?

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?

justus · Answer

As we see this is a quadratic equation.  So we can write it as c(x)=ax^2+bx+c.

The points are (2,23) ,(4,55) and(10,247). With these points we can make equations for each one.

Point one equation: 
23  = 4a + 2b + c
Point two equation:
55 = 16a + 4b + c
Point three equation:
247 = 100a+10b+c.

To solve all three equations we have: 
32 = 12a + 2b
16 = 6a + b
192 = 84 a + 6b
32 = 14a + b
We now have: a=2  b=4 c=7

The quadratic equation is c(x)= 2x^2+4x+7
When x is 8 we have 
c(x)= 2(8)^2+4(8)+7=167