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:-

Marginal Cost is the derivative of Total Cost:

$MC = \dfrac{dC}{dx}$

To get Total Cost, integrate the Marginal Cost.

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$C(x) = \int \left(56 + \dfrac{3}{2}x\right) dx$

$C(x) = 56x + \dfrac{3}{2} \cdot \dfrac{x^2}{2} + K$

$C(x) = 56x + \dfrac{3}{4}x^2 + K$

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Fixed cost is the cost when no units are produced, i.e., $x = 0$:

$C(0) = 56(0) + \dfrac{3}{4}(0)^2 + K = K$

Since fixed costs $= 115$:

$K = 115$

$C(x) = 56x + \dfrac{3}{4}x^2 + 115$

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For $x = 50$:

$C(50) = 56(50) + \dfrac{3}{4}(50)^2 + 115$

$= 2800 + \dfrac{3}{4}(2500) + 115$

$= 2800 + 1875 + 115$

$= 4790$

Therefore, the total cost of producing 50 units $= \text{Rs. } 4790$