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# The Total Cost Function for a Production is Given by C ( X ) = 3 4 X 2 − 7 X + 27 Find the Number of Units Produced for Which M.C. = A.C - Mathematics

Sum

The total cost function for a production is given by C(x) = 3/4 x^2 - 7x +  27
Find the number of units produced for which M.C. = A.C
(M.C. = Marginal Cost and A. C. = Average Cost.)

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#### Solution

C(x) = 3/4 x2  - 7x + 27              .....(1)

M.C = 3/2 x -7                         ....(2)

A.C = (C(x))/x = 3/4x -7 + 27/x
Given that, . . M C AC

therefore 3/2x - 7 = 3/4x - 7+27/x

therefore 3/2x - 3/4x = 27/x

therefore 3/4x = 27/x

therefore x^2 = 9xx4 =36|
therefore x = 9+6  units

Concept: Application of Calculus in Commerce and Economics in the Profit Function and Breakeven Point
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