Question

The marginal cost of the production of the commodity is 30 + 2x, it is known that fixed costs are ₹ 200, find

1. The total cost.
2. The cost of increasing output from 100 to 200 units.

Answer 1

Given: M.C. = 30 + 2x

i. We know, `M.C. = (dC)/dx`

⇒ `(dC)/dx = 30 + 2x`

Intergrating both sides w.r.t. x

`int (dC)/dx dx = int (30 + 2x) dx`

⇒ `C = 30x + (2x^2)/2 + k`

⇒ C = 30x + x² + k

ii. It is given that,

When x = 0, C = 200

∴ 200 = 0 + 0 + k

⇒ k = 200

∴ Total cost C(x) = 30x + x² + 200.