Maharashtra State BoardHSC Commerce 12th Board Exam
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The Cost C of Producing X Articles is Given as C=X3-16x2+47x. - Mathematics and Statistics

Sum

The cost C of producing x articles is given as C = x3-16x2 + 47x.  For what values of x, with the average cost is decreasing'?  

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Solution

C = x3 - 16x2 + 47x. 

Average cost CA = `"C"/"x" = ("x"^3 - 16"x"^2 + 47"x")/"x"`

∴ C = x2 - 16x + 47

Differentiating w.r.t. x 

`"dC"_"A"/"dx" = 2"x" - 16`

Cis decreasing if `"dC"_"A"/"dx" < 0`

i.e. 2x - 16 < 0 

i.e. 2x < 16 

i.e. x < 8

∴ Average cost Cis decreasing for x < 8.

  Is there an error in this question or solution?
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