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Math Help - Please help solve this completly

  1. #1
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    Please help solve this completly

    Hi there. New member here, I hope someone can help with this problem.

    The president of a company producing water pumps has gathered data that suggests that the average cost in dollars of producing x pumps will be
    C(x)=x^2-21x+100.Determine the number of pumps that the company needs to produce in order to have an average cost to 28$ per pump.

    Can't factor It what to do?
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  2. #2
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    Re: Please help solve this completly

    Quote Originally Posted by MathQuestion82 View Post
    Hi there. New member here, I hope someone can help with this problem.

    The president of a company producing water pumps has gathered data that suggests that the average cost in dollars of producing x pumps will be
    C(x)=x^2-21x+100.Determine the number of pumps that the company needs to produce in order to have an average cost to 28$ per pump.

    Can't factor It what to do?
    The cost to manufacture x pumps is

    $C(x)=x^2-21x+100$

    If the average cost is \$28 per pump then the total cost for x pumps is $28x$

    so

    $C(x)=x^2-21x+100=28x$

    Just rearrange this and apply the quadratic formula to solve for the roots of this equation.

    I'm actually seeing two valid answers though one is more realistic than the other.
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  3. #3
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    Re: Please help solve this completly

    Quote Originally Posted by romsek View Post
    The cost to manufacture x pumps is

    $C(x)=x^2-21x+100$

    If the average cost is \$28 per pump then the total cost for x pumps is $28x$

    so

    $C(x)=x^2-21x+100=28x$

    Just rearrange this and apply the quadratic formula to solve for the roots of this equation.

    I'm actually seeing two valid answers though one is more realistic than the other.
    So this is not correct?

    x^2 - 21x + 100 = 28
    x^2 - 21x + 100 - 28 = 0
    x^2 - 21x + 72 = 0

    x= 21/2 +- V(21/2)^2 -72

    V represents square root.

    x= 10.5+-V38.25
    x=10.5+-6.1844658438

    x1=4.315341562
    x2=16.68465844

    similar problem someone did it like me
    SOLUTION: Hi, please help me answer this question: The president of a company producing water pumps has gathered data suggesting that the average cost in dollars producing x units per hou

    Of course doesn't mean it's correct. But are you 100%?

    Thanks for the help
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  4. #4
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    Re: Please help solve this completly

    No, because like you are told, the cost depends on how many pumps are made. 1 would be 28 dollars, but 2 would be 56. x amount of them would be $28x .
    Thanks from MathQuestion82
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  5. #5
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    Re: Please help solve this completly

    ok you are pro. so the answer is 2 and 47 ? weird answer.
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  6. #6
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    Re: Please help solve this completly

    This is not a wonderfully worded or designed question. You have not told us what course you are taking, which might help us give you the best answer.

    As the question is written, C is not total cost but average cost per unit. Calling it A might be less confusing if in fact this is supposed to be a function describing the average cost per unit.

    So $x^2 - 21x + 100 = 28 \implies x^2 - 21x + 72 = 0 \implies x = \dfrac{21 \pm \sqrt{(-21)^2 - 4 * 1 * 72}}{2} = \dfrac{21 \pm \sqrt{153}}{2} \implies $

    $x \approx 17\ or\ x \approx 4.$

    HOWEVER, I think romsek and ProveIt are correct that C(x) is supposed to be a total cost function. One reason that I think so is that an average cost function usually looks like:

    $A(x) = g(x) + \dfrac{F}{x},$ where F stands for the fixed costs and $g(x) = C(x) - F.$

    In that case, the proper equation is total cost divided by number produced equals average cost, or

    $28 = \dfrac{C(x)}{x} = \dfrac{x^2 - 21x + 100}{x} \implies 28x = x^2 - 21x + 100 \implies x^2 - 49x + 100 = 0 \implies$

    $x = \dfrac{49 \pm \sqrt{*-49)^2 - 4 * 1 * 100}}{2} = \dfrac{49 \pm \sqrt{2001}}{2} \implies x \approx 2\ or\ x \approx 47.$

    Now if this is a problem in economics, you should already know that an equilibrium solution requires that marginal cost be rising.

    Marginal cost $= 2x - 21 > 0 \implies x \approx 47.$

    I HATE this problem.
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