A company produces ‘x’ units of geometry boxes in a day. If the raw material of one geometry box costs Rs. 2 more than square of the number of boxes produced in a day, cost of transportation is half the number of boxes produced in a day, also the cost incurred on storage is Rs. 150 per day. The marginal cost (in Rs.) when 70 geometry boxes are produced in a day is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 14,702.50
The raw material of one box costs \(x^2 + 2\), so for x boxes:
\(\text{raw material} = x\left(x^2 + 2\right) = x^3 + 2x\)
Adding transportation \(\frac{x}{2}\) and storage 150, the total cost is
\( \displaystyle C(x) = x^3 + 2x + \frac{x}{2} + 150 = x^3 + \frac{5x}{2} + 150 \)
The marginal cost is the derivative of the total cost:
\( \displaystyle MC = C'(x) = 3x^2 + \frac{5}{2} \)
At x = 70:
\(MC = 3\times 4900 + 2.5 = 14702.5\)
So the marginal cost is Rs. 14,702.50.