Find the total cost of producing 6 widgets.
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 costs $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.
If c(x) is a quadratic function, then c(x)=A×x2+B×x+C, where A, B, and C are constants. Our job here is to find the constants.
c(2)=23=A∗22+B∗2+C
c(4)=103=A∗42+B∗4+C
c(10)=631=A∗102+B∗10+C
So we have:
23=4A+2B+C
103=16A+4B+C
631=100A+10B+C
If we solve that, we get A = 6, B = 4, C = -9.
Thus, since c(x)=A×x2+B×x+C:
c(x)=6x2+4x−9
Now we just use the function for x=6.
c(6)=6×62+4×6−9
c(6)=231 dollars.
If c(x) is a quadratic function, then c(x)=A×x2+B×x+C, where A, B, and C are constants. Our job here is to find the constants.
c(2)=23=A∗22+B∗2+C
c(4)=103=A∗42+B∗4+C
c(10)=631=A∗102+B∗10+C
So we have:
23=4A+2B+C
103=16A+4B+C
631=100A+10B+C
If we solve that, we get A = 6, B = 4, C = -9.
Thus, since c(x)=A×x2+B×x+C:
c(x)=6x2+4x−9
Now we just use the function for x=6.
c(6)=6×62+4×6−9
c(6)=231 dollars.
