Question

 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.) 

Answer 1

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`