Question

The marginal cost function of x units of a product is given by 2MC= 3x² -10x +3x² The cost of producing one unit is Rs. 7. Find the cost function and average cost function. 

Answer 1

Let the total cost function be (C_x)
`therefore` Marginal cost Mc = `(dc)/dx`
`therefore (dc)/dx= 3x^2 - 10x+3`          .........(1)

`therefore c(x) = int (3x^2 - 10x + 3)dx`
          `= 3((x^3)/3)- 10(x^2 /2)+3x + A`
                     C(x) = x³ - 5x² + 3x + A          ........(2)
                     If n = 1 , C(1) = 7
`therefore  1 - 5 + 3 + A = 7`
`therefore  A = 7 + 5 - 4 = 8`
`therefore C(x) = x^3- 5x^2 +3x + 8`            .....(3)
Also, the average cost function is given by
`(C(x))/x =x^2 - 5x + 3 +8/x`          .....(4)