A company produces 'x' units of geometry boxes in a day. If the raw material of one geometry box costs ₹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 ₹150 per day. The marginal cost (in ₹) 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
Raw material cost = $x(x^2+2)=x^3+2x$
Transportation cost = $\frac{x}{2}$
Storage cost = 150
Total cost: $C(x)=x^3+2x+\frac{x}{2}+150$
$=x^3+\frac{5x}{2}+150$
Marginal Cost = $\frac{d}{dx}C(x)$
$=\frac{d}{dx}(x^3+\frac{5x}{2}+150)$
$=3x^2+\frac{5}{2}$
MC at $x=70$
$⇒3(70)^2+\frac{5}{2}$
$=14700+2.5$
$=14702.5$