A company has determined that when x hundred dulcimers are​ built, the average cost per dulcimer can be estimated by ​C(x)=0.2x(squared)−2.6x+9.950​, where​ C(x) is in hundreds of dollars. What is the minimum average cost per dulcimer and how many dulcimers should be built to achieve that​ minimum?

Question

The minimum average cost per dulcimer is ​$______. I have gotten this wrong twice and I only have one more try tonight :(

Answer 1

the graph of a quadratic equation is a parabola

when you are looking for a minimum, the parabola generally opens upward, with a minimum at the vertex
... this means a negative coefficient for the 2nd order (squared) term
... this is not the case with the equation you have

there seems to be something amiss

Answer 2

This is the question word for word on MyMathLab. The title of the chapter it is from is "Problem Solving and Quadratic Functions"

Answer 3

sorry, my train of thought derailed ...

the vertex is on the axis of symmetry
... the equation (for the axis) is ... x = -b / 2a
... in this case ... x = -(-2.6) / (2 * .2) = 6.5

min # of dulcimers is ... 650

solve C(650) to find the min ave cost of dulcimers