If the manufacturer's marginal cost function is \( 100\left(\displaystyle\frac{1}{\sqrt{x}}+50\right) \) , then the cost involved to increase production from 25 units to 100 units is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 3,76,000
The marginal cost is \( \frac{dC}{dx} \), so the extra cost is the definite integral of MC from 25 to 100:
\( \displaystyle \int_{25}^{100}100\left(x^{-1/2}+50\right)dx=100\Big[2\sqrt{x}+50x\Big]_{25}^{100} \)
\( \displaystyle =100\big[(2\cdot 10+5000)-(2\cdot 5+1250)\big] \)
\( \displaystyle =100(5020-1260) \)
\( \displaystyle =100\times 3760 \)
\( \displaystyle =376000 \)
So the cost is Rs. 3,76,000.