Algebra

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Aki's Bicycle designs has determined that when x hundred bicyles are built, the average cost per bicycle is given by C(x)=0.6^2-0.5x+4.021, where C(x) is in hundreds of dollars. How many biccles should the shop build to minimize the average cost per bicycle?

The shop should build _____ bicycles.

Could you please help me!!!!

  • Algebra -

    Don't you mean

    C(x)=0.6 x^2 - 0.5x + 4.021 ?

    I think you left out an x.
    Since you are not taking calculus, I will assume that you are supposed to answer this question by turning C(x) into a "perfect square" plus a constant.

    C(x)= 0.6 x^2 - 0.5x + 4.021
    0.6 [x^2 - (5/6)x + (5/12)^2] + 3.916
    = 0.6(x - 5/12)^2 + 3.916

    This is a minimum when x = 5/12. that means the number of bicyles is (5/12)*100 = 41.7

    Pick x = 0.42 instead of 0.41, since it is closer to 5/12 and 100x must be an integer.

    Proof: If x = 0.41, C(x) = 3.91686
    if x = 0.42, C(x) = 3.91684
    if x = 0.43, C(x) = 3.91694

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