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?
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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) = ?