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?

anonymous · Answer

Marcos, you're told you have a quadratic function, and you're give the x- and y-values at three points.  If you assume the function has the form$$y=ax^2+bx+c$$and sub in each corresponding x and y, you'll end up with three linear equations in three unknowns.  You can solve this system exactly; i.e. you can solve for a, b and c.  

Once you have a, b and c, you have your quadratic cost function and you can then answer the question of how much it is going to cost to produce 8 widgets; i.e. c(8) = ?