The marginal cost (MC) of producing \( x \) units of an item in a factory is given by \( \mathrm{MC}=0.006x^2-0.001x+4 \).
If the fixed cost is Rs. 1000, then the cost of producing 200 units will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 17,780
The total cost function is the integral of the marginal cost, and the constant of integration is the fixed cost:
\( \displaystyle C(x)=\int(0.006x^2-0.001x+4)\,dx \)
\( \displaystyle =0.002x^3-0.0005x^2+4x+K \)
Fixed cost = C(0) = K = 1000:
\( \displaystyle C(x)=0.002x^3-0.0005x^2+4x+1000 \)
At x = 200:
\( \displaystyle C(200)=0.002(8{,}000{,}000)-0.0005(40{,}000)+4(200)+1000 \)
\( \displaystyle =16{,}000-20+800+1000 \)
\( \displaystyle =17{,}780 \)
The cost of producing 200 units is Rs. 17,780.