The marginal cost of production of x units of a commodity is $56 +\frac{3}{2}x$. 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
GivenMarginal cost: $MC = 56 + \frac{3}{2}x$
Fixed cost: $FC = 115$
Total cost: $TC = FC + \int MC \, dx$
$\int (56 + \frac{3}{2}x) dx = 56x + \frac{3}{4}x^2$
Total cost for 50 units:
$TC = 115 + 56\cdot 50 + \frac{3}{4}\cdot 50^2$
$TC = 115 + 2800 + \frac{3}{4}\cdot 2500 = 115 + 2800 + 1875 = 4790$