The marginal cost of production of x units of a commodity is \(56 + \displaystyle\frac{3}{2}x\). It is known that fixed costs are Rs. 115. Then the total cost of producing 50 units is:-
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 4790
The total cost is the integral of the marginal cost:
\( \displaystyle C(x) = \int\left(56 + \frac{3}{2}x\right)dx = 56x + \frac{3}{4}x^2 + k \)
At x = 0 only the fixed cost remains, so the constant of integration is the fixed cost: C(0) = k = 115.
\( \displaystyle C(x) = 56x + \frac{3}{4}x^2 + 115 \)
\( \displaystyle C(50) = 56(50) + \frac{3}{4}(2500) + 115 \)
\(= 2800 + 1875 + 115 = 4790\)
So the total cost of producing 50 units is Rs. 4790.