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 x^{2 }- 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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