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lilfayfay

  • 3 years ago

The cost of producing x units of a certain product is given by: C=10,000 + 5x+ 1/9 x^2 Find the value of x that gives the minimum average cost

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  1. mayankdevnani
    • 3 years ago
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    You have a cost function for x units given by: C = 10,000 + 5x + (1/9)x^2 Now, the cost per unit is going to be that same function divided by x. Let's call this function U: U = 10,000/x + 5 + (1/9)x To find the minimum total cost, you need to find the minimum of this function. Analyzing the derivatives should get you the answer you need: U' = -10,000/(x^2) + 1/9 U'' = 20,000/(x^3) http://mathforum.org/library/drmath/view/53402.html By examining U'= 0, we find that x = 300 is a critical point. Further, since U'' is positive, the function must be at a minimum at that point.

  2. lilfayfay
    • 3 years ago
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    @mayankdevnani can you help me with another problem pls? ^^

  3. lilfayfay
    • 3 years ago
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    wait how did u get U"=20,000/x^3?

  4. lilfayfay
    • 3 years ago
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    nvm

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