The marginal cost of producing x units is C'(x) = 10.6x. The fixed cos

1.	The marginal cost of producing x units is C'(x) = 10.6x. The fixed cost is Rs. 50. The selling price per unit is Rs.5. Find (i) total cost function (ii) total revenue function and (iii) profit function.
Answer» Given C'(x) = 10.6x C'(x) = ∫(10.6x) dx + k = 10.6 x²/2 + k = 5.3x² + k The fixed cost is Rs. 50 (i.e.) when x = 0, c = 50 ⇒ k = 50 Hence cost function C = 5.3x² + 50 Now, total revenue = number of units sold × price/unit Since x be the number of units sold. The selling price is Rs.5 per unit. Revenue R(x) = 5x Profit P = Total revenue – Total cost = 5x – (5.3x² + 50) = 5x – 5.3x² – 50

The marginal cost of producing x units is C'(x) = 10.6x. The fixed cost is Rs. 50. The selling price per unit is Rs.5. Find (i) total cost function (ii) total revenue function and (iii) profit function.

Answer»

Given C'(x) = 10.6x

C'(x) = ∫(10.6x) dx + k

= 10.6 x²/2 + k

= 5.3x² + k

The fixed cost is Rs. 50

(i.e.) when x = 0, c = 50 ⇒ k = 50

Hence cost function C = 5.3x² + 50

Now, total revenue = number of units sold × price/unit

Since x be the number of units sold.

The selling price is Rs.5 per unit.

Revenue R(x) = 5x

Profit P = Total revenue – Total cost

= 5x – (5.3x² + 50)

= 5x – 5.3x² – 50