Algebra

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

  1. 9
asked by Joy
  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

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

    posted by Joy
  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

    posted by scott

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